In a dutch engagement control system for engagement and disengagement of transmission of a rotational force between a mainshaft and a countershaft, when clutch engagement control is executed based on the determination that rotational speeds of both the shafts agree with each other, even if unexpected variations in countershaft rotational speed result from torsion occurring downstream of the countershaft in a drive system and/or the like, smooth engagement control is implemented. A control value of countershaft rotational speed at each time is updated and managed. If a threshold value is exceeded by a difference between a countershaft rotational speed actual measured value and the preceding control value, the threshold value is added to the preceding value to obtain the control value. If the threshold value does not exceed the difference, the actual measured value at this time is set as a control value without any change.