A multi-joint hinge has a mounting element which can be fixed to an appliance body and a hinge part which can be fixed to a door and which is held pivotably on the mounting element via a joint mechanism with a plurality of joint levers. The hinge part is biased in the closing direction via a spring and at least one linear damper with a damper housing and a piston rod displaceable relative to the damper housing is provided which brakes a closing movement of the hinge part. The linear damper is arranged with the damper housing in a rotationally fixed manner via a holding element within a lever and the holding element is fixed to a lever of the joint mechanism. The piston rod can be pushed into the damper housing via an actuating element which is arranged on a further lever of the joint mechanism.