  In this paper, the asymptotic behavior of the solutions of a monotone problem
posed in a locally periodic oscillating domain is studied. Nonlinear monotone
boundary conditions are imposed on the oscillating part of the boundary whereas
the Dirichlet condition is considered on the smooth separate part. Using the
unfolding method, under natural hypothesis on the regularity of the domain, we
prove the weak $L^2$-convergence of the zero-extended solutions of the
nonlinear problem and their flows to the solutions of a limit distributional
problem.
