Many theoretical models of slender prismatic beams in a cross-wind have been developed during last decades. They mostly follow various types of the linear approach. Therefore their applicability is very limited especially for prediction of the system post-critical behavior. The subject considered in this paper represents a part of a complex theoretical background of the general nonlinear model which would enable fo predict any system reaction in the pre- and post-critical domain. In particular, the aeroelastic self-induced oscillaton of a mechanical system with generalized single degree of freedom (SDOF) is discussed. The motion is described by an ordinary differential equation of Duffing type with special generalized aero-elastic damping of Van der Pol type. A new semi-analytical approach is introduced to identify the limit cycles both stable and unstable. The latter are not possible to be identified by means of experiments nor by the numerical integration. and Obsahuje seznam literatury