Several data storage devices for use with flexible magnetic disks are daisy chained to a central processing unit via a controller to be selectively driven thereby for data transfer with the magnetic disks. Each storage device has a motor control circuit for setting the magnetic disk into rotation when a corresponding DRIVE SELECT signal from the controller assumes a prescribed state for the first time after and IN USE signal common to all the storage devices has assumed a prescribed state. Further the motor control circuits sets the magnetic disk out of rotation when the DRIVE SELECT signal assumes the prescribed state for the first time after the IN USE signal has been set out of the prescribed state. Thus the storage devices are held out of operation to avoid unnecessary power consumption even after the production of the IN USE signal, until the associated DRIVE SELECT signals are applied. Moreover, once set into operation, the storage devices remain so despite changes in the states of the DRIVE SELECT signals during the production of the IN USE signal, allowing ready access for data transfer.