In a tape recorder/reproducer apparatus, particularly where a low-inertia highly responsive drive train is used, tape speed control means including a variable-speed motor for the drive train energized through a closed-loop servosystem in which the actual output speed of the motor is monitored by a sensor and compared to a reference, to closely control the motor speed in accordance with the reference. The reference is provided by a freely supported capstan which senses actual tape speed at the tape head and produces an output which is compared to a predetermined reference representative of the desired tape speed, such that the motor is servo controlled to satisfy a predetermined tape speed function.