Novel robust finite time stabilizing algorithms are proposed in [1] for a nonlinear first and second order systems under sufficiently large or linear growing input disturbance. In the present paper the proposed algorithms are generalized under simultaneous presence of large input and output disturbances. This problem is not trivial and complicated, because simultaneous compensation of input and output disturbances leads to the failure of objective or the loss of closed-loop system stability. Thus, in the paper we synthesis algorithms and define the class of disturbances such that the closed-loop system preserves the stability and goal is fulfilled. The control scheme is based on the disturbance compensation, relying on the dirty differentiation, and sliding mode approaches. The sufficient conditions of the closed-loop system stability under admissible disturbances are given. Simulation results illustrate efficiency of the proposed schemes and support theoretical results.