The systems with 3/2 and two degrees of freedom close to nonlinear integrable are considered. For systems with 3/2 degrees of freedom the results of research of structure of resonant zones (passable, partially passable and impassable; non-degenerate and degenerate) are presented. The method of averaging, and also methods of the qualitative theory and the theory of bifurcation of dynamic systems is used. If for systems with 3/2 degrees of freedom in resonant cases the average systems are two-dimensional, for systems with two degrees of freedom are three-dimensional determined on solid torus. The results on research of such partially average systems are discussed. Alongside with it the completely average systems are resulted, and the problem of global behavior is discussed. The consideration is illustrated on an example of the equations such as Duffing ? Van-der-Pole.
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