diff --git a/core/src/main/java/hudson/model/AperiodicWork.java b/core/src/main/java/hudson/model/AperiodicWork.java
index bccb84b8eaba69c384a102242f3352e0e9e1f0a9..b46ac8fc0e4782c28ce0df3c581906da66fe1d35 100644
--- a/core/src/main/java/hudson/model/AperiodicWork.java
+++ b/core/src/main/java/hudson/model/AperiodicWork.java
@@ -74,7 +74,11 @@ public abstract class AperiodicWork extends SafeTimerTask implements ExtensionPo
      * By default it chooses the value randomly between 0 and {@link #getRecurrencePeriod()}
      */
     public long getInitialDelay() {
-        return Math.abs(RANDOM.nextLong())%getRecurrencePeriod();
+        long l = RANDOM.nextLong();
+        // Math.abs(Long.MIN_VALUE)==Long.MIN_VALUE!
+        if (l==Long.MIN_VALUE)
+            l++;
+        return Math.abs(l)%getRecurrencePeriod();
     }
 
     @Override
diff --git a/core/src/main/java/hudson/model/PeriodicWork.java b/core/src/main/java/hudson/model/PeriodicWork.java
index 6faec3840b538e0b3557dc4aa48abf91e45a657d..9bb02abd3a4fb4a3f884a597ac6f3f7723929a2c 100644
--- a/core/src/main/java/hudson/model/PeriodicWork.java
+++ b/core/src/main/java/hudson/model/PeriodicWork.java
@@ -75,7 +75,11 @@ public abstract class PeriodicWork extends SafeTimerTask implements ExtensionPoi
      * By default it chooses the value randomly between 0 and {@link #getRecurrencePeriod()}
      */
     public long getInitialDelay() {
-        return Math.abs(RANDOM.nextLong())%getRecurrencePeriod();
+        long l = RANDOM.nextLong();
+        // Math.abs(Long.MIN_VALUE)==Long.MIN_VALUE!
+        if (l==Long.MIN_VALUE)
+            l++;
+        return Math.abs(l)%getRecurrencePeriod();
     }
 
     /**