A transmission gearbox for a rotary-wing aircraft includes a main gearbox and a variable speed gearbox in meshing engagement with the main rotor gearbox. The variable speed gearbox permits at least two different RPMs for the main rotor system without disengaging the engine(s) or changing engine RPMs. The variable speed gearbox includes a clutch, preferably a multi-plate clutch, and a freewheel unit for each engine. A gear path drives the main gearbox in a “high rotor speed mode” when the clutch is engaged to drive the main rotor system at high rotor rpm for hover flight profile. A reduced gear path drives the main gearbox in a “low rotor speed mode” when the clutch is disengaged and power is transferred through the freewheel unit, to drive the main rotor system at lower rotor rpm for high speed flight. The variable speed gearbox may be configured for a tail drive system that operates at a continuous speed, a tail drive system that changes speed with the main rotor shaft or for no tail drive system.