This paper deals with the most important characteristics of a generic bidimensional dissipative system, subject to a small external excitation in resonance or in quasi-resonance with the primary resonance frequency of the system. In particular, the appearance of limit cycles and bifurcations is considered, by means of an asymptotic perturbation method quite different from the standard perturbation theory. We demonstrate that its behavior looks like the behavior of a universal model system. In view of it, we identify a sufficient condition to obtain a doubly periodic motion, when a second little frequency appears, in addition to the primary resonance frequency. Comparison with the numerical solution obtained by the Runge-Kutta-Fehlberg method confirms the validity of our analysis.