An actuator arrangement for the axial displacement of an actuation member by means of a drive force which is generated by an electric machine, in particular for a shift-clutch arrangement of a multi-step gear change transmission. The actuation member is mounted axially displaceably on a rotary shaft. The electric machine has a stator fixed to a housing and a rotor which is coupled to the actuation member and is arranged coaxially with respect to the actuation member. The rotor is coupled to the actuation member with a form fit in the axial direction. Here, the rotor or the actuation member has a radial projection which engages into a radial groove of the other part.