It is predicted theoretically that because of its time‐dependent mechanical properties, the rolling behavior of a wear fragment of viscoelastic material trapped between two moving surfaces is complex. If the moving surfaces are smooth and unlubricated, the fragment may either roll with a velocity equal to half the relative velocity between the surfaces, or it may reach a terminal rolling velocity beyond which increases in surface speed cannot drive it. If the surfaces are lubricated, the tractive force tending to roll the fragments arises from the friction of surface asperities sliding through the fragment. The rolling behavior then depends on the ratio of the size of the asperity to the size of the fragment. A critical value of this ratio exists. Above it, the fragment rolls at a velocity always slightly less than half that of the surfaces because of slip. Below the critical ratio, the fragment cannot be driven beyond a certain maximum velocity. Slip always takes place between the fragment and the surface, and increases with increasing surface velocity. Beyond the maximum rolling velocity, an increase of surface velocity leads to a decrease in the rolling velocity of the fragment.