The invention relates to a change-under-load transmission having an input shaft (1) and an output shaft (6), each carrying a pair of gearwheels (2, 3; 4, 5). A composite layshaft comprises two pairs of coaxial shafts (7, 8; 9, 10) which are aligned axially with one another. At their adjacent ends the shafts carry friction coupling elements (25, 31 and 25, 30) which have effective coupling faces (25', 31'; 26' 30'). At their remote ends each of the coaxial shafts carries a gearwheel (23, 27; 24, 28) which is in permanent mesh with an associated one of the gear wheels on the respective input or output shaft. Between the adjacent ends of the two pairs of coaxial shafts a central friction coupling element (32) is positioned so as to be freely slidable axially with respect to the coaxial shafts. Correspondingly positioned ones (7, 9 in FIG. 1; 8, 10 in FIG. 2) of the two pairs of shafts are supported so as to be axially inwardly slidable independently of one another out of a rest position into which they are biassed by springs (21, 22 in FIG. 1; 45, 46 in FIG. 2), and the other shaft (8, 10 in FIG. 1; 7, 9 in FIG. 2) are axially immovable. In the rest position of the shafts the effective coupling faces (30' 31' in FIG. 1, 47' 48' in FIG. 2) of the coupling elements on the slidable shafts are nearer the central coupling disc than the coupling faces (25' 26' in FIG. 1 and 49', 50' in FIG. 2) of the coupling elements on the axially immovable shafts.