A hybrid-electric propulsion system for an aircraft is provided herein that can include a propulsor and a turbomachine comprising a high pressure turbine drivingly coupled to a high pressure compressor through a high pressure spool. An auxiliary power unit can be operably coupled with a starter motor. An electrical system can comprise a first electric machine coupled to the turbomachine. The first electric machine can be separate from the starter motor. A controller can be 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.