global bifurcation patterns between sets of structurally stable systems have been completely understood on the basis of such analysis, since several decades ago." More recently much progress has been done applying these ideas to higher dimensional systems." However, quanti-tative details of the phase portrait are usually obtained by means of numerical work because approximate analytical methods are not useful, in general, for this purpose. The first aim of this paper is to display the global bifurcation behavior of a model which, contrarily to the usual case, has an exact general solution in terms of elementary functions. The existence of such a solution will give us a chance to describe analytically the whole structure of the phase portrait. This model is interesting from the physical point of view because of its capability to model nonlinear oscillations in both the quasiharmonic and relaxation regimes. It consists of a …