A variable-speed drive system for a tiltrotor, the variable-speed drive system comprising: a first propulsion system comprising a first fixed-drive system coupled to a first proprotor that is operable between a helicopter mode and an airplane mode, wherein the first fixed-drive system comprises a first fixed engine and a first variable-speed gearbox, the first fixed engine and the first variable-speed gearbox coupled to one another by a first spiral bevel gearbox; a second propulsion system comprising a second fixed-drive system coupled to a second proprotor that is operable between a helicopter mode and an airplane mode, wherein the second fixed-drive system comprises a second fixed engine and a second variable-speed gearbox, the second fixed engine and the second variable-speed gearbox coupled to one another by a second spiral bevel gearbox; an interconnect shaft coupled between the first variable-speed gearbox and the second variable-speed gearbox providing a torque path that enables a single engine to provide torque to both the first proprotor and the second proprotor; wherein the first variable-speed gearbox and the second variable-speed gearbox each comprise: an input shaft coupled to the spiral bevel gearbox of the respective fixed engine; an output shaft coupled to the respective proprotor (22, 23); a high-speed clutch integrated into a high-speed gear train, the high-speed gear train having an input coupled to the input shaft and an output coupled to the output shaft; a low-speed clutch integrated into a low-speed gear train, the low-speed gear train having an input coupled to the input shaft and an output coupled to the output shaft; and an accessory drive having an accessory-drive input, wherein the accessory drive is a variable-ratio drive which matches the speed of the input shaft without regard to a speed of the output shaft, wherein the accessory-drive input is coupled to the input shaft through a high-speed drive gear to match the accessory drive to an engine speed and the accessory drive is coupled to the output shaft by an overrunning clutch. a first propulsion system comprising a first fixed-drive system coupled to a first proprotor that is operable between a helicopter mode and an airplane mode, wherein the first fixed-drive system comprises a first fixed engine and a first variable-speed gearbox, the first fixed engine and the first variable-speed gearbox coupled to one another by a first spiral bevel gearbox; a second propulsion system comprising a second fixed-drive system coupled to a second proprotor that is operable between a helicopter mode and an airplane mode, wherein the second fixed-drive system comprises a second fixed engine and a second variable-speed gearbox, the second fixed engine and the second variable-speed gearbox coupled to one another by a second spiral bevel gearbox; an interconnect shaft coupled between the first variable-speed gearbox and the second variable-speed gearbox providing a torque path that enables a single engine to provide torque to both the first proprotor and the second proprotor; wherein the first variable-speed gearbox and the second variable-speed gearbox each comprise: an input shaft coupled to the spiral bevel gearbox of the respective fixed engine; an output shaft coupled to the respective proprotor (22, 23); a high-speed clutch integrated into a high-speed gear train, the high-speed gear train having an input coupled to the input shaft and an output coupled to the output shaft; a low-speed clutch integrated into a low-speed gear train, the low-speed gear train having an input coupled to the input shaft and an output coupled to the output shaft; and an accessory drive having an accessory-drive input, wherein the accessory drive is a variable-ratio drive which matches the speed of the input shaft without regard to a speed of the output shaft, wherein the accessory-drive input is coupled to the input shaft through a high-speed drive gear to match the accessory drive to an engine speed and the accessory drive is coupled to the output shaft by an overrunning clutch. an input shaft coupled to the spiral bevel gearbox of the respective fixed engine; an output shaft coupled to the respective proprotor (22, 23); a high-speed clutch integrated into a high-speed gear train, the high-speed gear train having an input coupled to the input shaft and an output coupled to the output shaft; a low-speed clutch integrated into a low-speed gear train, the low-speed gear train having an input coupled to the input shaft and an output coupled to the output shaft; and an accessory drive having an accessory-drive input, wherein the accessory drive is a variable-ratio drive which matches the speed of the input shaft without regard to a speed of the output shaft, wherein the accessory-drive input is coupled to the input shaft through a high-speed drive gear to match the accessory drive to an engine speed and the accessory drive is coupled to the output shaft by an overrunning clutch.