A transmission system that is used in conjunction with a microturbine engine for propelling an aircraft body, such as a propeller-based fixed-wing aircraft or a rotor-based vertical lift aircraft, or for a wide variety of other applications. The output shaft of the microturbine engine preferably operates at a rotational speed in a range between 72,000 RPM and 150,000 RPM with an output power between 150 HP and 5 HP (and most preferably operates in an extended range between 50,000 RPM and 200,000 RPM with an output power between 200 HP and 5 HP). The two reduction stages provide a reduction ratio preferably having a value of at least 19, and most preferably greater than 24. The transmission system is of small-size preferably having a maximum diameter less than twelve inches. The two stages of the transmission system may comprise any one (or parts of) of a number of configurations, including an in-line lay shaft configuration, an in-line star-star configuration an offset star-spur configuration, an offset compound idler configuration, an inline traction-internal gear configuration, and an inline traction planetary gear configuration. Preferably, the input stage of the transmission system is self-equilibrating such that first shaft can be supported without bearings and is operably coupled to the output shaft of the microturbine engine by an outside diameter piloted spline coupling mechanism. For vertical lift applications, a single traction stage along with a bevel gear assembly or other shaft transmission mechanism can be used to provide the necessary RPM reduction.