In an automatic transmission for a vehicle such as an automobile having a speed stage shifting mechanism including parallelly arranged first and second hydraulically operated input clutches and adapted to provide the 3rd speed stage in which the first and second input clutches C.sub.1 and C.sub.2 are both engaged (though the engagement of the clutch C.sub.1 in the 3rd speed stage is not essential unless engine brake availability is required) and the overdrive 4th stage in which the clutch C.sub.1 is disengaged and the clutch C.sub.2 is engaged, the clutch C.sub.1 in the 3rd speed stage being not essential unless engine a hydraulic control device has a switching over valve 330 for switching over supply of a hydraulic pressure to the first clutch C.sub.1 between a first mode of relatively slowing supplying the hydraulic pressure to the first clutch C.sub.1 and a second mode of relatively quickly supplying the hydraulic pressure to the first clutch C.sub.1 according to engine output power so as to select the second mode when engine output power is higher than a determinate power level as in the downshifting by kickdown and to select the first mode when engine output power is less than the determinate power level as in the overdrive inhibition.