In the paper we study the problem of control under the magnitude and rate limitations imposed to the control input in application to flight control systems. In the case of the control surfaces magnitude and rate limitations, the self-oscillations of considerable amplitude may occur, which is often reffered to as "the loss of stability in large". If the aircraft is weathercock stable, then two limit cycles may co-exist: a stable cycle of small magnitude and an unstable one with a large magnitude. If the aircraft is weathercock unstable, then one cycle from a pair of stable limit cycles with small magnitude may arise. In addition, there is also an unstable limit cycle, the presence of which makes it necessary to study the stability of the aircraft with automatic longitudinal control "in large", i.e. when large disturbances act onto the aircraft and move the aircraft out of the border of unstable limit cycle. Influence of such nonlinearities as "saturation" may cause the so-called "Pilot Involved Oscillations", which degrades the piloting of the aircraft. For studying the processes that occur in nonlinear flight control systems (including nonlinear oscillations), a simple computer simulation is an unreliable tool, which can lead to wrong conclusions. To obtain reliable simulation results, analytical validation of the condition of the uniqueness of the limit solution should be fulfilled or special analytical and numerical methods to find the hidden oscillations should be employed. In the paper, the analytical-numerical procedure and numerical methods for localization and parameter determination of hidden oscillations in nonlinear systems are described, and their applications are demonstrated for an analysis of dynamics for various kinds of flying vehicles, such as yaw control of non-rigid rocket carrier, automatic control of aircraft angle of attack, as well as man-machine aircraft-pilot system, supplied by stability augmentation system.