diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsBashforthIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsBashforthIntegrator.java
index 07d205c35..0985508da 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsBashforthIntegrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsBashforthIntegrator.java
@@ -146,10 +146,12 @@ public class AdamsBashforthIntegrator extends AdamsIntegrator {
     /**
      * Build an Adams-Bashforth integrator with the given order and step control parameters.
      * @param nSteps number of steps of the method excluding the one being computed
-     * @param minStep minimal step (must be positive even for backward
-     * integration), the last step can be smaller than this
-     * @param maxStep maximal step (must be positive even for backward
-     * integration)
+     * @param minStep minimal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
+     * @param maxStep maximal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
      * @param scalAbsoluteTolerance allowed absolute error
      * @param scalRelativeTolerance allowed relative error
      * @exception IllegalArgumentException if order is 1 or less
@@ -166,10 +168,12 @@ public class AdamsBashforthIntegrator extends AdamsIntegrator {
     /**
      * Build an Adams-Bashforth integrator with the given order and step control parameters.
      * @param nSteps number of steps of the method excluding the one being computed
-     * @param minStep minimal step (must be positive even for backward
-     * integration), the last step can be smaller than this
-     * @param maxStep maximal step (must be positive even for backward
-     * integration)
+     * @param minStep minimal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
+     * @param maxStep maximal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
      * @param vecAbsoluteTolerance allowed absolute error
      * @param vecRelativeTolerance allowed relative error
      * @exception IllegalArgumentException if order is 1 or less
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsIntegrator.java
index fc38b9ba7..8332d5df4 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsIntegrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsIntegrator.java
@@ -39,10 +39,12 @@ public abstract class AdamsIntegrator extends MultistepIntegrator {
      * @param name name of the method
      * @param nSteps number of steps of the method excluding the one being computed
      * @param order order of the method
-     * @param minStep minimal step (must be positive even for backward
-     * integration), the last step can be smaller than this
-     * @param maxStep maximal step (must be positive even for backward
-     * integration)
+     * @param minStep minimal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
+     * @param maxStep maximal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
      * @param scalAbsoluteTolerance allowed absolute error
      * @param scalRelativeTolerance allowed relative error
      * @exception IllegalArgumentException if order is 1 or less
@@ -62,10 +64,12 @@ public abstract class AdamsIntegrator extends MultistepIntegrator {
      * @param name name of the method
      * @param nSteps number of steps of the method excluding the one being computed
      * @param order order of the method
-     * @param minStep minimal step (must be positive even for backward
-     * integration), the last step can be smaller than this
-     * @param maxStep maximal step (must be positive even for backward
-     * integration)
+     * @param minStep minimal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
+     * @param maxStep maximal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
      * @param vecAbsoluteTolerance allowed absolute error
      * @param vecRelativeTolerance allowed relative error
      * @exception IllegalArgumentException if order is 1 or less
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsMoultonIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsMoultonIntegrator.java
index 7178f2ef0..fd780931f 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsMoultonIntegrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/AdamsMoultonIntegrator.java
@@ -162,10 +162,12 @@ public class AdamsMoultonIntegrator extends AdamsIntegrator {
     /**
      * Build an Adams-Moulton integrator with the given order and error control parameters.
      * @param nSteps number of steps of the method excluding the one being computed
-     * @param minStep minimal step (must be positive even for backward
-     * integration), the last step can be smaller than this
-     * @param maxStep maximal step (must be positive even for backward
-     * integration)
+     * @param minStep minimal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
+     * @param maxStep maximal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
      * @param scalAbsoluteTolerance allowed absolute error
      * @param scalRelativeTolerance allowed relative error
      * @exception IllegalArgumentException if order is 1 or less
@@ -182,10 +184,12 @@ public class AdamsMoultonIntegrator extends AdamsIntegrator {
     /**
      * Build an Adams-Moulton integrator with the given order and error control parameters.
      * @param nSteps number of steps of the method excluding the one being computed
-     * @param minStep minimal step (must be positive even for backward
-     * integration), the last step can be smaller than this
-     * @param maxStep maximal step (must be positive even for backward
-     * integration)
+     * @param minStep minimal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
+     * @param maxStep maximal step (sign is irrelevant, regardless of
+     * integration direction, forward or backward), the last step can
+     * be smaller than this
      * @param vecAbsoluteTolerance allowed absolute error
      * @param vecRelativeTolerance allowed relative error
      * @exception IllegalArgumentException if order is 1 or less
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.java
index 12835c51f..45f4f02e4 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/AdaptiveStepsizeIntegrator.java
@@ -92,10 +92,12 @@ public abstract class AdaptiveStepsizeIntegrator
   /** Build an integrator with the given stepsize bounds.
    * The default step handler does nothing.
    * @param name name of the method
-   * @param minStep minimal step (must be positive even for backward
-   * integration), the last step can be smaller than this
-   * @param maxStep maximal step (must be positive even for backward
-   * integration)
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
    * @param scalAbsoluteTolerance allowed absolute error
    * @param scalRelativeTolerance allowed relative error
    */
@@ -122,10 +124,12 @@ public abstract class AdaptiveStepsizeIntegrator
   /** Build an integrator with the given stepsize bounds.
    * The default step handler does nothing.
    * @param name name of the method
-   * @param minStep minimal step (must be positive even for backward
-   * integration), the last step can be smaller than this
-   * @param maxStep maximal step (must be positive even for backward
-   * integration)
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
    * @param vecAbsoluteTolerance allowed absolute error
    * @param vecRelativeTolerance allowed relative error
    */
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54Integrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54Integrator.java
index 97866aacf..59dd85ef9 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54Integrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince54Integrator.java
@@ -93,10 +93,12 @@ public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator {
 
   /** Simple constructor.
    * Build a fifth order Dormand-Prince integrator with the given step bounds
-   * @param minStep minimal step (must be positive even for backward
-   * integration), the last step can be smaller than this
-   * @param maxStep maximal step (must be positive even for backward
-   * integration)
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
    * @param scalAbsoluteTolerance allowed absolute error
    * @param scalRelativeTolerance allowed relative error
    */
@@ -109,10 +111,12 @@ public class DormandPrince54Integrator extends EmbeddedRungeKuttaIntegrator {
 
   /** Simple constructor.
    * Build a fifth order Dormand-Prince integrator with the given step bounds
-   * @param minStep minimal step (must be positive even for backward
-   * integration), the last step can be smaller than this
-   * @param maxStep maximal step (must be positive even for backward
-   * integration)
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
    * @param vecAbsoluteTolerance allowed absolute error
    * @param vecRelativeTolerance allowed relative error
    */
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853Integrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853Integrator.java
index 958a06c40..c16e08bc1 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853Integrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/DormandPrince853Integrator.java
@@ -205,10 +205,12 @@ public class DormandPrince853Integrator extends EmbeddedRungeKuttaIntegrator {
 
   /** Simple constructor.
    * Build an eighth order Dormand-Prince integrator with the given step bounds
-   * @param minStep minimal step (must be positive even for backward
-   * integration), the last step can be smaller than this
-   * @param maxStep maximal step (must be positive even for backward
-   * integration)
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
    * @param scalAbsoluteTolerance allowed absolute error
    * @param scalRelativeTolerance allowed relative error
    */
@@ -222,10 +224,12 @@ public class DormandPrince853Integrator extends EmbeddedRungeKuttaIntegrator {
 
   /** Simple constructor.
    * Build an eighth order Dormand-Prince integrator with the given step bounds
-   * @param minStep minimal step (must be positive even for backward
-   * integration), the last step can be smaller than this
-   * @param maxStep maximal step (must be positive even for backward
-   * integration)
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
    * @param vecAbsoluteTolerance allowed absolute error
    * @param vecRelativeTolerance allowed relative error
    */
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/EmbeddedRungeKuttaIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/EmbeddedRungeKuttaIntegrator.java
index 313127d7f..66192f819 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/EmbeddedRungeKuttaIntegrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/EmbeddedRungeKuttaIntegrator.java
@@ -99,10 +99,12 @@ public abstract class EmbeddedRungeKuttaIntegrator
    * @param a internal weights from Butcher array (without the first empty row)
    * @param b propagation weights for the high order method from Butcher array
    * @param prototype prototype of the step interpolator to use
-   * @param minStep minimal step (must be positive even for backward
-   * integration), the last step can be smaller than this
-   * @param maxStep maximal step (must be positive even for backward
-   * integration)
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
    * @param scalAbsoluteTolerance allowed absolute error
    * @param scalRelativeTolerance allowed relative error
    */
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/GraggBulirschStoerIntegrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/GraggBulirschStoerIntegrator.java
index 4aaa148e5..e141f4589 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/GraggBulirschStoerIntegrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/GraggBulirschStoerIntegrator.java
@@ -155,10 +155,12 @@ public class GraggBulirschStoerIntegrator extends AdaptiveStepsizeIntegrator {
    * Build a Gragg-Bulirsch-Stoer integrator with the given step
    * bounds. All tuning parameters are set to their default
    * values. The default step handler does nothing.
-   * @param minStep minimal step (must be positive even for backward
-   * integration), the last step can be smaller than this
-   * @param maxStep maximal step (must be positive even for backward
-   * integration)
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
    * @param scalAbsoluteTolerance allowed absolute error
    * @param scalRelativeTolerance allowed relative error
    */
diff --git a/src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java b/src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java
index dbf0ae9ae..289d51068 100644
--- a/src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java
+++ b/src/main/java/org/apache/commons/math/ode/nonstiff/HighamHall54Integrator.java
@@ -66,10 +66,12 @@ public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
 
   /** Simple constructor.
    * Build a fifth order Higham and Hall integrator with the given step bounds
-   * @param minStep minimal step (must be positive even for backward
-   * integration), the last step can be smaller than this
-   * @param maxStep maximal step (must be positive even for backward
-   * integration)
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
    * @param scalAbsoluteTolerance allowed absolute error
    * @param scalRelativeTolerance allowed relative error
    */
@@ -82,10 +84,12 @@ public class HighamHall54Integrator extends EmbeddedRungeKuttaIntegrator {
 
   /** Simple constructor.
    * Build a fifth order Higham and Hall integrator with the given step bounds
-   * @param minStep minimal step (must be positive even for backward
-   * integration), the last step can be smaller than this
-   * @param maxStep maximal step (must be positive even for backward
-   * integration)
+   * @param minStep minimal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
+   * @param maxStep maximal step (sign is irrelevant, regardless of
+   * integration direction, forward or backward), the last step can
+   * be smaller than this
    * @param vecAbsoluteTolerance allowed absolute error
    * @param vecRelativeTolerance allowed relative error
    */