A connecting device of a vehicle drive-train, located outside a variable-speed transmission, for rotationally coupling a shaft to a drive-train element. A sliding sleeve is rotationally fixed on the shaft but slides axially between first and second positions. In the first position, the shaft is rotationally disengaged from the drive-train element and, in the second position, they are rotationally coupled. An actuator displaces the sliding sleeve between the first and second positions, with a shift groove along a peripheral contour of the sliding sleeve and engagement members for engaging in the groove. The sliding sleeve can rotate and move axially relative to the engagement members and the groove is shaped as a curved guiding such that, when the engagement members engage in the groove and the sliding sleeve rotates relative to the engagement member, the sliding sleeve moves axially between the first and second positions by virtue of the groove.