This paper presentsan adaptive actuator failure compensation method, which compensates for uncertainties due to unknown actuator failures for redundant manipulator systems. The method is first developed for manipulators whose joints are concurrently actuated. While physical realization of concurrently actuated manipulators and the advantages of their use have been understood before, in this paper failure modeling. controller structure, and adaptive update rules for handling uncertainties from the actuator failures are studied. The adaptive actuator failure compensation method is then expanded for a cooperating , multiple manipulator system with uncertain actuator failures. Dynamic equations of Such a multiple manipulator system in the task space are derived and the adaptive actuator failure compensation problem is formulated in the task space, for which a compensation controller structure is proposed with stable adaptive parameter update laws. The adaptive control scheme is able to compensate for the uncertainties of system parameters and actuator failures in a more general sense. For both cases. closed-loop system stability and asymptotic tracking are proved, despite uncertain system failures.