An electrical machine comprises a rotor without windings, a stator having an armature winding (24, 25) and a field winding (10) for generating a magnetomotive force in a direction extending transversely of the magnetomotive force generated by the armature winding. An electronic circuit (40) is provided for controlling the current in the armature winding (24, 25) such that periods in which a magnetomotive force in one direction is associated with a first current pulse alternate with periods in which a magnetomotive force in the opposite direction is associated with a second current pulse. A position sensor is provided for monitoring the rotational position of the rotor and for supplying output signals at a rate dependent on the speed of rotation of the rotor. Furthermore a control system supplies control signals to the circuit (40) to control the current in the armature winding (24, 25) in response to the output signals. The control system uses a control signal of extended duration at the beginning of the first current pulse on start-up of the motor from rest as compared with the duration of the control signals produced over the remainder of the first current pulse during acceleration of the rotor. Such an arrangement produces efficient starting from rest, and enables control of acceleration, no-load speed, loaded torque-speed characteristics of the machine to be achieved with simple on-off control of armature and field switching devices, so that the control circuitry can be produced at relatively low cost. Simplification of the control circuitry is further ensured by the fact that such control can be effected without current sensing.