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In this paper we study the limit behavior of the solution uϵ of a parametric variational inequality, governed by a nonlinear differential operator, the gradient operator ∇ being replaced by another operator ∇ϵ, with the positive parameter ϵ (ϵ→0). Generalizing earlier results of Courilleau and Mossino [P. Courilleau, J. Mossino, Compensated compactness for nonlinear homogenization and reduction of...