In a vehicular automatic transmission, a coast downshift is executed in an appropriate engine-braking state and with a light gearshift shock. While predetermined conditions for the execution of the downshift are met, an oil pressure to be fed to a clutch (c12 in FIG. 1) on the side of a gearshift output stage (a lower speed stage) is controlled, for example, in order that the input shaft speed (turbine speed01 in FIG. 1) of the automatic transmission may agree with a desired value adapted to keep the weak engine-braking state.