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This work concerns about forward-backward multivalued stochastic systems.First of all, we prove one average principle for general stochasticdifferential equations in the $L^{2p}$ ($p\geq 1$) sense. Moreover, for $p=1$ aconvergence rate is presented. Then combining general stochastic differentialequations with backward stochastic variation inequalities, we establish theother average principle for backward stochastic variation inequalities in the$L^{2}$ sense through a time discretization method. Finally, we apply ourresult to nonlinear parabolic partial differential equations and obtain thehomogenization of them.

Average principles for forward-backward multivalued stochastic systems and homogenization for systems of nonlinear parabolic PDEs