The paper is devoted to the global bifurcation analysis of the models of strongly nonlinear forced or autonomous dynamical systems with one or several-degree-of-freedom by direct numerical and/or analytical methods. A new approach for the global bifurcation analysis for strongly nonlinear dynamical systems, based on the ideas of Poincaré, Birkhoff and Andronov, is proposed. The main idea of the approach is a concept of complete bifurcation groups and periodic branch continuation along stable and unstable solutions, named by the author as a method of complete bifurcation groups (MCBG). The article is illustrated using four archetypal forced dynamical systems with one degree-of-freedom. They are Duffing model with positional force f(x) = x + x^3, Duffing double-well potential driven system, pendulum driven system and piecewise-linear (bilinear soft impact) driven dynamical system.