A method of starting and apparatus for starting a multiphase electrical machine is disclosed. The aim is to reduce oscillatory pulsation in torque generated by the motor and inrush current that occurs shortly after start-up. The starting method comprises the steps of first connecting at least one, but less than all, of a plurality of windings to a respective phase-shifted supply voltage at a controlled point in the supply phase. Then, after a controlled delay following the first connection, connecting the or each remaining winding of the machine a respective phase-shifted supply voltage. The invention has particular application to multiphase (most usually, 3-phase) motors. However, it can also be applied to other electrical machines, such as generators and transformers. The method can be performed at initial start-up or, in the case of application to a motor, at Y-delta switchover.