A propulsion system for an aircraft includes a propulsor; a turbomachine mechanically coupled to the propulsor for driving the propulsor during a combustion operating mode of the propulsion system and mechanically decoupled from the propulsor during an electric operating mode of the propulsion system; and an electrical power source. The propulsion system further includes an electric machine, the electric machine being electrically coupled to the electrical power source and mechanically coupled to the propulsor during the electric operating mode of the propulsion system such that the electric machine drives the propulsor during the electric operating mode of the propulsion system.