A steerable auxiliary nose undercarriage (2) for a rotary wing aircraft (1); the undercarriage (2) being retractable substantially rearwards. In the undercarriage (2), an oscillating system (13) presents a elevation stroke (58) about its hinged front end (52) that is greater than a shock absorbing stroke (59), and a shock-absorbing actuator (9) possesses retraction means for going beyond a high abutment position of the oscillating system (13) so that the oscillating system (13) and the shock-absorbing actuator (9) provide both a shock-absorption function and an undercarriage retraction function.