A downhole rotational rate control apparatus is disclosed, adapted for coupling to the lower end of a drill string, and includes a progressive cavity (PC) pump or motor, multiple fluid flow paths, and a flow control valve for controlling fluid flow in the flow paths. Drilling mud flowing downward through the drill string is partially diverted to flow through the PC pump or motor and, in turn, the PC pump or motor speed is controlled by the flow control valve. The control valve can be actuated by a control motor in response to inputs from a sensor assembly in an electronics section. The PC pump or motor drives a controlled downhole device at a specific zero or non-zero rotational rate. By varying the rotational rate of the PC pump or motor relative to the rotational rate of the drill string, the tool face orientation or non-zero rotational speed of the controlled device in either direction can be varied in a controlled manner.