A tape recording and/or reproducing apparatus includes first and second motors for driving takeup and supply reels, respectively. The first motor is energized during fast forward mode to drive the takeup reel at a speed higher than the normal playback speed to feed the tape cassette from the supply reel to the takeup reel. The rotational speed of the supply reel, which is initially low and increases as a function of time, is sensed by a speed detector which develops a voltage proportional to the sensed speed. A comparator is provided to detect when the voltage reaches a predetermined value to complete a feedback control circuit to feed the voltage to the second motor. A counter torque is produced in the second motor to retard the torque produced by the first motor. By the feedback operation the supply reel is subsequently driven at a constant speed. The tape transport speed initially increases until the feedback control is effected and subsequently decreases as a function of time as the tape approaches its end to allow a tape stopping mechanism a sufficient time to operate before the tape end overruns the transducer head.