A method of operating a hybrid engine for an aircraft, the hybrid engine having a thermal engine and an electric motor. The method includes verifying, using an engine control unit of the hybrid engine, that a selected power level is under a predetermined threshold for operation of the hybrid engine in a sub-idle hybrid mode. The method further includes operating the hybrid engine in the sub-idle hybrid mode, using the engine control unit, by controlling the thermal engine to operate in a standby mode, and by controlling the electric motor to operate in an active mode wherein the electric motor provides a majority of a propulsive power to the aircraft, wherein in the standby mode the thermal engine operates in a sub-idle condition to provide at most minimal propulsive power to the aircraft.