The device for flying an aircraft includes a first unit for determining a control value corresponding to an instruction value representing the actuation of a control member by a pilot, a second unit for determining an effective control value corresponding to the instruction value which is actually applied to the aircraft, a third unit for automatically controlling the aircraft, a fourth unit for computing an auxiliary control value, which is closer to the effective controlled value, and a fifth unit for monitoring the control value and for detecting a pilot induced oscillation, where the automatic control is carried out with the aid of the controlled effective value and the auxiliary control value in the case of the detection of the pilot induced oscillation.