A perturbation theory has recently been developed for treating the diffration of light, with surface polariton resonant excitation, from a bigrating surface. The theory is an approximation, to first order in the grating height, of an earlier theory based on the Rayleigh hypothesis. The perturbation theory holds for arbitrary polarization and for arbitrary plane of incidence with respect to the grating directions. It is, however, limited to treating only the possibility of two simultaneous resonant evanescent waves, whereas four are possible at normal incidence on a square grating, and three are possible on a rectangular grating. The present work generalizes the earlier work to allow for a four fold (or three fold) resonance. This extension also allows one now to determine the complex dispersion relation for surface-polaritons, for wavevectors at the intersection of two Brillouin zone boundary lines (not possible in the previous formulation). Keywords: Smith Purcell radiation; Bigrating; Grating; Surface plasmon; Polariton.