The nonlinear dynamical systems are widely used in the engineering, but their qualitative behavior hasn’t been investigated enough. Therefore the aim of this work is to study new nonlinear effects by the method of complete bifurcation groups (MCBG) in archetypal models of the nonlinear dynamical systems with one degree of freedom, which are sufficiently close to the real models used in dynamics of the machines and mechanisms. The method is based on the ideas of Poincaré, Birkhoff, Andronov and others [1-6]. The MCBG allows in a new way examining some sections of theory of catastrophes, with greater authenticity deciding the tasks of nonlinear diagnostics [7]. In the important problem of controlling chaos in the dynamical systems [8, 9] it is also succeeded to propose new solutions on the basis of MCBG. In the near future this approach can find a wide application at the decision of aerospace tasks dynamical tasks of medicine and ecology, and also modern tasks of economy and control. For illustration of main ideas of the method and possibility of obtaining on its basis the new results in this work are used simple considerably nonlinear models with one degree of freedom and with external harmonic excitation. New bifurcation sub-groups, received by the MCBG, are so-called rare attractors (RA), complex protuberances, unstable periodic infinitiums (UPI) allow to do complete bifurcation analysis for the nonlinear models. It is shown that UPI bifurcation groups formed in the model chaotic behaviour such as usual chaotic or rare chaotic attractors, or chaotic transients. The main feature of the MCBG is that it uses nT-branches continuation without their break in bifurcation points and connected with protuberances born from some bifurcation points by period doubling.