The results associated with the nonlinear theory of surface magnetoplasma waves (SW) propagating across an external magnetic field at a solid-state plasma-metal interface are presented. In a weak nonlinearity approximation using a formalism of third-order nonlinear susceptibilities the nonliner frequency shift of the SW is calculated. The possible nonlinear mechanisms which influence the SW propagation are discussed. In several cases the comparison of the obtained results with previous papers gives a possibility to estimate the third order nonlinear susceptibility of the nonlinear medium bounded by a metal.