A variable-speed gearbox (26) for a tiltrotor with fixed engine (24) and rotating proprotor (28) includes an input shaft (34) coupled to the respective fixed engine (24), an output shaft (36) coupled to the respective proprotor (28); a high-speed clutch (74) integrated into a high-speed gear train (40), the high-speed gear train (40) having an input coupled to the input shaft (34) and an output coupled to the output shaft (36); and a low-speed clutch (76) integrated into a low-speed gear train (42), the low-speed gear train (42) having an input coupled to the input shaft (34) and an output coupled to the output shaft (36). The high-speed clutch (74) and the low-speed clutch (76) 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 (40, 42) in an overrunning condition when the output rotates faster than the input of the respective gear train (40, 42). The low-speed clutch (76) can be permanently engaged. In accordance to some embodiments the variable-speed gearboxes (26) may include an accessory drive (50).