In a transmission for an automotive vehicle, a control system for a direct-coupling mechanism for mechanically engaging input and output members of a hydraulic power transmission. An operating fluid pressure regulator controls operating fluid pressure applied to a hydraulically operating portion of the direct-coupling mechanism, and the direct-coupling mechanism applies an engaging force corresponding to the operating fluid pressure thus controlled to the input and output members. A vehicle speed sensor detects the speed of the vehicle, and a slip sensor detects the value of a predetermined parameter indicative of an amount of relative slip between the input and output members. When the detected vehicle speed falls between a first predetermined value and a second predetermined value larger than the first predetermined value and at the same time the detected value of the predetermined parameter is outside a predetermined range, a control device causes the operating fluid pressure regulator to vary the magnitude of the operating fluid pressure so that the predetermined parameter falls within the predetermined range.