Abstract: A method of starting a gas turbine engine with a synchronous multiphase alternating current (AC) dynamoelectric machine with a rotor and a stator that allows re-engagement of a starting operation at non-zero rotor speeds comprises the steps of: applying electrical excitation to the rotor; measuring electromotive force (EMF) generated in the stator; determining rotor speed, acceleration and position from the measured EMF by sensorless means; initiating closed-loop sensorless position controlled power to the stator if the determined rotor speed is at least a pre-determined minimum closed-loop sensorless re-engagement speed; initiating open-loop position controlled power to the stator if the determined rotor speed is less than the pre-determined minimum closed-loop sensorless re-engagement speed but at least a predetermined minimum open-loop re-engagement speed and the determined rotor acceleration is no more than a pre-determined maximum open-loop re-engagement acceleration; and initiating open-loop zero-speed