This article develops a new framework of adaptive actuator failure compensation control for cooperative manipulator systems with parameter uncertainties in addition to actuator failures, and designs and analyzes effective actuator failure compensation schemes for such robotic systems. The new adaptive control design uses an integration of multiple individual failure compensators and direct adaptation to handle various types of uncertainties in such robotic systems. The design can also be used for concurrent actuator failure cases, to expand the capability of adaptive actuator failure compensation. With a complete proof and performance analysis, it is shown that the proposed control scheme guarantees the desired closed-loop stability and asymptotic output tracking, despite actuator failures whose patterns, time instants and values are all unknown. Simulation results of a benchmark cooperative manipulator system are presented to verify the desired control performance of the system with both typical constant and square-wave actuator failure signals.