A hybrid propulsion system comprising: a heat engine configured to drive a heat engine shaft thereof; an electric motor configured to drive an electric motor shaft thereof; a turbine having a shaft; a compressor; and a transmission system including at least one gearbox, wherein the transmission system is configured to receive rotational input power from each of the heat engine shaft and the electric motor shaft and to convert the rotation input power to output power; and wherein: the heat engine shaft and the electric motor shaft are connected for common rotation; and the at least one gearbox includes: a combining gearbox connecting to a common output shaft of the electric motor and the heat engine, and to the shaft of the turbine, for providing rotational output power to an output shaft of the combining gearbox; characterised in that the combining gearbox is configured to combine rotational input power from the heat engine, electric motor, and turbine; and in that the at least one gearbox further includes a reduction gearbox connected to the output shaft, wherein the compressor is connected to be driven on the output shaft. a heat engine configured to drive a heat engine shaft thereof; an electric motor configured to drive an electric motor shaft thereof; a turbine having a shaft; a compressor; and a transmission system including at least one gearbox, wherein the transmission system is configured to receive rotational input power from each of the heat engine shaft and the electric motor shaft and to convert the rotation input power to output power; and wherein: the heat engine shaft and the electric motor shaft are connected for common rotation; and the at least one gearbox includes: a combining gearbox connecting to a common output shaft of the electric motor and the heat engine, and to the shaft of the turbine, for providing rotational output power to an output shaft of the combining gearbox; characterised in that the combining gearbox is configured to combine rotational input power from the heat engine, electric motor, and turbine; and in that the at least one gearbox further includes a reduction gearbox connected to the output shaft, wherein the compressor is connected to be driven on the output shaft. the heat engine shaft and the electric motor shaft are connected for common rotation; and the at least one gearbox includes: a combining gearbox connecting to a common output shaft of the electric motor and the heat engine, and to the shaft of the turbine, for providing rotational output power to an output shaft of the combining gearbox; characterised in that the combining gearbox is configured to combine rotational input power from the heat engine, electric motor, and turbine; and in that the at least one gearbox further includes a reduction gearbox connected to the output shaft, wherein the compressor is connected to be driven on the output shaft. a combining gearbox connecting to a common output shaft of the electric motor and the heat engine, and to the shaft of the turbine, for providing rotational output power to an output shaft of the combining gearbox; characterised in that the combining gearbox is configured to combine rotational input power from the heat engine, electric motor, and turbine; and in that the at least one gearbox further includes a reduction gearbox connected to the output shaft, wherein the compressor is connected to be driven on the output shaft.