A motor vehicle powertrain system according to this invention controls the magnitudes of torque produced by multiple power sources that drive the vehicle wheels. The system includes a source of pressurized fluid, and a pump/motor driveably connected to the wheels, which is driven in a motoring mode by fluid from the fluid source and has a variable volumetric displacement that changes in response to displacement of the accelerator pedal. An engine, driveably connected to the wheels, includes a throttle that opens and closes in response to displacement of the accelerator pedal. A controller controls operation of the engine and pump/motor such that they produce torque at various magnitudes. The system determines a magnitude of desired wheel torque, a maximum available engine wheel torque, a maximum available pump/motor wheel torque, a difference in magnitude between the desired wheel torque and the maximum available pump/motor wheel torque, operates the pump/motor as a motor such that the pump/motor produces a magnitude of wheel torque that is equal to the lesser of the desired wheel torque and the maximum available pump/motor wheel torque, and operates the engine such that the engine produces a magnitude of wheel torque that is equal to the lesser of the maximum available engine wheel torque and the difference in torque magnitude.