A shifting device of a motor vehicle transmission having a driveshaft (2) in the form of a hollow shaft with radial bores (5, 6, 7, 8). At least one drive output element (3) is arranged on the driveshaft (2), a shifting element (4) is arranged to move axially within the hollow shaft (2), and coupling elements, in the form of balls (9, 10, 11, 12), move radially within the radial bores (5, 6, 7, 8; 24). The drive output element (3) can be coupled to and decoupled from the driveshaft (2) by axial displacement of the shifting element (4) and radial displacement of the balls (9, 10, 11, 12). The shifting element is in the form of a shifting piston (4) and the hollow shaft (2) is in the form of a shifting cylinder (2aa).