A method of controlling a direct-coupling mechanism of hydraulic power transmission means having an input member and an output member, of an automatic transmission for an automotive vehicle, said direct-coupling mechanism being operable to mechanically engage and disengage said input member and said output member with and from each other, wherein a transmission capacity of said direct-coupling mechanism is controlled such that the value of a predetermined parameter indicative of an amount of relative slip between said input member and said output member lies within a predetermined reference range, the method comprising the steps of:
- (1) detecting the value of said predetermined parameter;
- (2) comparing the detected value of said predetermined parameter with said predetermined reference range;
- (3) determining a desired value of said transmission capacity and a predetermined period of time on the basis of the result of said comparison such that as the detected value of said predetermined parameter approaches said predetermined reference range, a rate of change in said transmission capacity is decreased;
- and (4) controlling the transmission capacity to the determined desired value thereof for the determined predetermined period of time.