System Information
Win7/64

Blender Version
Worked: 2.67b
Broken: 2.68a
Broken: blender-2.70-be980b9-win64

Short description of error
Whenever an object belongs to group A, it can not be added to group B if there is already an instance of group A belonging to group B because the message "Could not add the group because of dependency cycle detected" occurs.

Exact steps for others to reproduce the error

1. Open
   GroupCyclicDependency.blend64 KBDownload
2. Add an instance of group "Arm" and rotate it by 180°
3. Make the body the parent of the group instance.
4. Add the group instance to the group "Person".
5. Select the two cylinders on the right and also try to add them to group "Person". This fails with the message that a dependency cycle is detected. IMO, this is a false alarm.