Abstract: A shaft coupling for a drive shaft (3), with a driving and a driven coupling component in which the driving or the driven coupling component is configured to form a cylindrical hollow coupling outer member (8) and the other coupling component configured to form a cylindrical coupling inner member (9), the two members being disposed so as to be coaxial with the longitudinal axis of the shaft coupling, and in which axially parallel grooves (27, 28) that are provided with right- and left-sided side walls (19, 20, 21, 22) are formed on the inner circumference of the coupling outer member (8) and on the outer circumference of the coupling inner member (9) for receiving rolling members (11) that drivingly and axially slidably interconnect the coupling outer member (8) and the coupling inner member (9), whereby the right- and left-sided side walls (19, 20, 21, 22) of the coupling inner member (8) and of the coupling outer member (9) are disposed side by side and mesh together thereby in such a manner that, together