A hybrid-electric propulsion system for an aircraft includes a propulsor and a turbomachine. The turbomachine includes a high pressure turbine drivingly coupled to a high pressure compressor through a high pressure spool. The hybrid electric propulsion system further includes an electrical system including a first electric machine, a second electric machine, and an electric energy storage unit electrically connectable to the first and second electric machines. The first electric machine is coupled to the high pressure spool of the turbomachine and the second electric machine is coupled to the propulsor for driving the propulsor to provide a propulsive benefit for the aircraft. The hybrid electric propulsion system also includes a controller configured to provide electrical power from an electric power source to the first electric machine to drive the first electric machine to start, or assist with starting, the turbomachine.