Abstract: A speed-changing transmission device for vehicles includes a speed-changing shaft connected to rear wheels and disposed at the rear side of an input shaft driven by an engine co-axially with the input shaft, a counter shaft mounted in parallel with the speed-changing shaft and driven by the input shaft, and forward and backward speed-changing gear systems through which the speed-changing gear is connected to the counter shaft to constitute a speed-changing transmission mechanism. A forward one-way clutch is disposed between the input shaft and the speed-changing shaft of the speed-changing mechanism. In the power transmission path formed by the backward speed-changing gear system, provided is a backward clutch and a backward one-way clutch parallel with the backward clutch. The connection between the engine and the speed-changing the speed is turned into "OFF" state during parking of the vehicle, so that an engine braking effect is obtained to prevent the vehicle from starting naturally.