A variable-speed gearbox for a tiltrotor with fixed engine and rotating proprotor includes an input shaft coupled to the respective fixed engine, an output shaft coupled to the respective proprotor; 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; and 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. The high-speed clutch and the low-speed clutch can be freewheeling clutches capable of disconnecting the output and the input of the respective gear train of the high and low-speed gear trains in an overrunning condition when the output rotates faster than the input of the respective gear train. The low-speed clutch can be permanently engaged. In accordance to some embodiments the variable-speed gearboxes may include an accessory drive.