The saturation of actuators is an essential nonlinearity, and the consideration of the bounded actuator torques during the design of the computed torque control (CTC) is a challenging task. In this study, the saturation of the actuator torques is treated as a temporary reduction of the number of independent control inputs. Consequently, a manipulator, which is fully actuated in the neighbor-hood of its desired motion, becomes underactuated when the intricate combinations of the actuator saturations occur. The cascade of two CTC algorithms is applied to resolve the problem of the temporary underactuation: the classical CTC method is self-interrupted and exchanged to a generalized CTC that is extended to underactuated systems. The corresponding control algorithm is applicable even in those cases of multi-body problems where the use of non-minimum set of coordinates provides the computationally efficient mathematical description together with servo-constraint based task definitions leading to differential algebraic equations.