An aircraft comprising a fixed structure, a fuselage mounted on the fixed structure and a tail unit system comprising a structural element housed inside the fuselage and mounted to be rotationally mobile relative to the fixed structure about a transverse axis of rotation parallel to a transverse axis of the aircraft. A first actuation system displaces the structural element in rotation about the transverse axis of rotation, on either side of the structural element. A horizontal tail unit has one end rotationally mobiley mounted on the structural element about a longitudinal axis of rotation parallel to a longitudinal axis of the aircraft and another end which extends out of the fuselage by passing through a window in the fuselage. For each horizontal tail unit, a second actuation system displaces the horizontal tail unit in rotation about the longitudinal axis of rotation.