A control apparatus (80; 122) for a vehicle (10; 100) provided with a drive power source (14, MG2; 102, MG), and a step-variable transmission (20; 110) which constitutes a part of a power transmitting path between the drive power source (14, MG2; 102, MG) and drive wheels (28; 116) and which is placed in a selected one of a plurality of speed positions (1st-4th) with engagement of a selected one or ones of a plurality of coupling devices (B, C), said control apparatus comprising: a transmission shifting control portion configured to implement a shifting action of the step-variable transmission (20; 110) from one of the plurality of speed positions to another of the plurality of speed positions, by controlling a releasing action of a releasing coupling device (C, B) and an engaging action of an engaging coupling device (C, B), the releasing coupling device (C, B) being one of the plurality of coupling devices (C, B) which has been placed in an engaged state before initiation of the shifting action, the engaging coupling device (C, B) being another of the plurality of coupling devices (C, B) which is to be placed in the engaged state after completion of the shifting action; a torque control portion configured to implement a feedback control to control an input torque (Tm, Ti) that is inputted to the step-variable transmission (20; 110), during the shifting action of the step-variable transmission (20; 110), such that a value (dωm/dt) representing a state of a rotary motion of an input rotary member (30; 124) of the step-variable transmission (20; 110) coincides with a target value that is dependent on a degree (Rpro) of progress of the shifting action of the step-variable transmission (20; 110); a vehicle-state determining portion configured to determine whether the drive wheels (28; 116) are slipped or not; and characterized by comprising a backup control portion configured to inhibit implementation of the feedback control, when it is determined that the drive wheels (28; 116) are slipped during the shifting action of the step-variable transmission (20; 110), and to compensate a transmitted torque (Tcb) to be transmitted through an initiative coupling device (C, B) which is one of the releasing coupling device (C, B) and the engaging coupling device (C, B) and which causes the shifting action to progress, such that the progress of the shifting action is facilitated by compensation of the transmitted torque (Tcb). a transmission shifting control portion configured to implement a shifting action of the step-variable transmission (20; 110) from one of the plurality of speed positions to another of the plurality of speed positions, by controlling a releasing action of a releasing coupling device (C, B) and an engaging action of an engaging coupling device (C, B), the releasing coupling device (C, B) being one of the plurality of coupling devices (C, B) which has been placed in an engaged state before initiation of the shifting action, the engaging coupling device (C, B) being another of the plurality of coupling devices (C, B) which is to be placed in the engaged state after completion of the shifting action; a torque control portion configured to implement a feedback control to control an input torque (Tm, Ti) that is inputted to the step-variable transmission (20; 110), during the shifting action of the step-variable transmission (20; 110), such that a value (dωm/dt) representing a state of a rotary motion of an input rotary member (30; 124) of the step-variable transmission (20; 110) coincides with a target value that is dependent on a degree (Rpro) of progress of the shifting action of the step-variable transmission (20; 110); a vehicle-state determining portion configured to determine whether the drive wheels (28; 116) are slipped or not; and characterized by comprising a backup control portion configured to inhibit implementation of the feedback control, when it is determined that the drive wheels (28; 116) are slipped during the shifting action of the step-variable transmission (20; 110), and to compensate a transmitted torque (Tcb) to be transmitted through an initiative coupling device (C, B) which is one of the releasing coupling device (C, B) and the engaging coupling device (C, B) and which causes the shifting action to progress, such that the progress of the shifting action is facilitated by compensation of the transmitted torque (Tcb).