The purpose of this paper is to study the nonlinear excitation of surface polaritons taking fully into account the damping of the active medium and the finite cross-section of the nonlinear polarization on the interface. This problem is solved using the guided wave calculation techniques where the EM field at the surface polariton frequency is expanded over a complete set of normal modes of the unperturbed interface. Using a "table method" we find that this set includes one guided mode, which is the surface polariton mode, and two classes of radiation modes. The expressions of all these modes are derived and interpreted physically. We then get the expression of the EM field excited at the surface polariton frequency inside and outside the pumped region and show that, in the general case, it is a mixture of all these normal modes. The end of the paper is mainly devoted to the study of the surface term occurring in the expression of the EM field at the surface polariton frequency: we point out the existence of a resonance phenomenon with two kinds of surface polariton modes: the "spatial" one and the "temporal" one. The corresponding dispersion curves, or resonance curves, are given and it is explained how each of them can be obtained experimentally.