A system for use in an exercise apparatus for synchronizing the movement of the upper limbs comprises a shaft mounted for rotation about its longitudinal axis, left and right pulleys mounted at opposed end portions of the shaft, and left and right handlebars respectively connected to the left and right pulleys and pivotable therewith about the longitudinal axis of the shaft. Left and right one-way clutches are provided for respectively transmitting a torque from the left and right pulleys to the shaft in one direction, while allowing the left and right pulleys to rotate freely relative to the shaft when driven in an opposite direction. First and second cables are connected in parallel between the left and right pulleys to communicate a movement imparted to one of the pulleys to the other pulley but in an opposite direction, thereby causing the handlebars to pivot in an inverted synchronized fashion.