Pilot-Induced Oscillation (PIO) is an instability resulting from the dynamic interaction between the pilot and the aircraft. In this paper, we present a general framework for the analysis of nonlinear PIO. The approach involves the computation of nonlinear phenomena such as Hopf bifurcation that lead to large changes in structural stability of the Pilot-Vehicle System (PVS). Flying qualities cliffs are associated with these nonlinear phenomena. Since PVS is a forced system, standard bifurcation analysis techniques are not directly applicable to the PIO problem. This difficulty is circumvented by augmenting the PVS dynamics with an asymptoticall y stable nonlinear oscillator. As examples, the X-15 PIO caused by ratelimiting and an F/A-18 PIO caused by nonlinear Category III triggers are considered. We computed limit cycle amplitudes as a function