In an automatic transmission for a vehicle such as an automobile having a speed stage shifting mechanism including parallelly arranged first and second input clutches C1, C2 and adapted to selectively engage the first and second input clutches in three ways of engaging the first input clutch C1 with the second input clutch C2 being disengaged to provide a certain first speed stage (2nd speed stage), engaging the second input clutch C2 with the first clutch C1 being disengaged to provide a certain second speed stage (4th speed stage) and engaging both the first and second clutches C1, C2 to provide a certain third speed stage (3rd speed stage), a hydraulic control device has a first valve (3-4 shift valve) for switching over connection of the first input clutch C1 with a hydraulic pressure supply 274 and a drain 280, a second valve (2-3 shift valve) for exchanging connection of the second input clutch C2 and a fail safe port 260 with a hydraulic pressure supply 246 and a drain 252, 253, and a passage 268 for connecting the drain for the first valve with the fail safe port 260 of the second valve so that at least one of the first and second input clutch is supplied with hydraulic pressure regardless of sticking of the first and/or the second valve.