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Summary form only given. The resonant nature of the excitation of surface electromagnetic waves (SEWs), i.e. the resonant dependence of the reflectivity on the incident radiation wavevector component parallel to the interface (surface), k, leads to the nonlinear phenomena arising and particularly optical bi- and multi-stability appearance at relatively small nonlinearities. At such nonlinearities the field induced variation of the SEW wavevector, K, becomes comparable with the width, Im(K), of the mentioned geometrical (angular) resonance. In the paper the theory of optical bi- and multistability at the excitation of TM-polarized SEWs via the Kretschmann attenuated total reflection (ATR) scheme (glass prism-metal film-dielectric) in which the dielectric exhibits a relatively small one- or two-photon resonant nonlinearity is presented. The system of equations describing the excitation of nonlinear SEWs is presented in general form for arbitrary type of nonlinearity by means of the SEW wavevector nonlinear term, K/sup NL/.