A method of starting a turbine engine at a first engine speed value which is lower than a second engine speed value designed for a normal engine starting operation, comprises varying a fuel flow into a combustor of the engine to start the engine in repeatedly alternating speed acceleration and deceleration cycles in order to create an engine speed augmentation in each of the speed acceleration and deceleration cycles, thereby achieving the second engine speed value while preventing the engine from being overheated, and then beginning the normal engine starting operation.