The invention relates to an electromechanical actuator for a vehicle brake comprising a body (4) in which are arranged an electric motor (5) and a threaded plunger cooperating via a helical link with a nut (8) driven in rotation by the electric motor (5). According to the invention, the nut (8) is mounted to move axially in the body (4) of the actuator between a rest position towards which the nut (8) is pushed back by elastic means, and an active position towards which the nut is displaced against the elastic means when a braking force is applied, the actuator further comprising means for detecting the axial displacement of the nut.