Summary: Limit cycle oscillations are complex vibrations of airframe surfaces for which the cause-and-effect relationships are poorly understood. This fundamental investigation of oscillations of a finite two-dimensional flexible plate considers unforced vibrations, as well as situations where motion is induced by a convected vortex, a pressure wave, or an unsteady boundary layer seperation on the moving plate. It is found that very complex vibration patterns can occur and, with increasing nonlinearity, essentially chaotic motion can develop. When the plate is forced at frequencies close to the natural frequencies of the linear problem, a nonlinear resonance phenomenon occurs leading to a complex limit cycle behavior.