We have obtained the solution of the stationary problem for P-polarized nonlinear surface polaritons (NLSP) near the interface of two media, one of which is optically linear and the other having an optical nonlinearity with saturation and a dielectric function of the form: ɛ=ɛxx=ɛzz=ɛ0+a|E|2/(1+b|E|2), where E is the amplitude of the electric field. On this basis the NLSP energy and propagation properties, the polarization structure and the localization depth of the NLSP field as well as the physically allowed region in the parameter space have been investigated for the case in which the parameter ɛ0 is positive, b is non-negative, and a and ɛ1 are negative (ɛ1 is the dielectric function of the linear medium); ɛ0>|ɛ1|.