In the paper two types of nonlinear limit-cycles oscillations in flight control systems, caused by typical static nonlinearities of the control surfaces actuators that arise in the flight of aircraft are considered: The elastic-flexural flutter of the wing and pilot induced oscillations (PIO), where interactions of a flight controller with a human pilot's dynamics can cause the origin instability. Hidden oscillations in the pilot-aircraft closed loop are studied and localized by means of the iterative analytical-numerical method. A problem of adaptive flutter suppression is studied and an opportunity of emerging the hidden oscillations due to controlling surface saturation in rate and magnitude is demonstrated.