Abstract: We consider variational inequalities with invertible operators in divergence form and with constraint set a.e. in where is a nonempty bounded open set in, p > 1, and are measurable functions. Under the assumptions that the operators G-converge to an invertible operator, = 0, and there exist functions such that a.e. in and we establish that the solutions us of the variational inequalities converge weakly in to the solution u of a similar variational inequality with the operator and the constraint set V. The fundamental difference of the considered case from the previously studied one in which is that, in general, the functionals do not converge to even weakly in and the energy integrals do not converge to. © Pleiades Publishing, Ltd. 2024. ISSN 1064-5624, Doklady Mathematics, 2024, Vol. 109, No. 1, pp. 62–65. Pleiades Publishing, Ltd., 2024. ISSN 1064-5624, Doklady Mathematics, 2024. Pleiades Publishing, Ltd., 2024.