An aircraft hybrid propulsion system (5) comprises an internal combustion engine (10) comprising a main drive shaft (24), an electric machine (28) comprising an electric machine rotor (78), a propulsor (12) mounted to a propulsor shaft (62), and a clutch arrangement configured to selectively couple each of the gas turbine engine main drive shaft (24) and electric machine rotor (78) to the propulsor drive shaft (62). The electric machine rotor (78) is mounted coaxially with the main drive shaft (24) and the clutch arrangement comprises a first overrunning clutch (52) configured to couple the main drive shaft (24) to the propulsor drive shaft (62), and a second overrunning clutch (54) configured to couple the electric machine rotor (78) to the propulsor drive shaft (62).