In this chapter, a special emphasis is given to approximate methods of solution of nonlinear equations (the small-parameter method, asymptotic methods). A relation between the Bubnov–Galerkin method with the Gauss’ principled is established. A detailed exposition is given to P. L. Kapitsa’s method of direct separation of motions, which at present is not adequately presented in textbooks. Theoretical results are clarified by solving a number of new examples. The last subsection is dedicated to strange attractors.