||Let X denote the space of all real, bounded double sequences, and let Ф∞,Γ, be, ∞-functions . Moreover, let Ψ be an increasing, continuous function for u ≥ 0 such that Ψ (0) = 0. In this paper we consider some spaces of double sequences provided with two-modular structure given by generalized variations and the translation operator. We apply the [fórmula disponible al document original] convergence in X(Ф,Ψ) in order to obtain an approximation theorem by means of the (m, n)-translation, i . e . a result of the form [fórmula disponible al document original] - 0 in an Orlicz sequence space IΓ.