We prove the existence of uniform attractors Aε in the space H 1 (R N ) for the nonautonomous nonclassical diffusion equationThe upper semicontinuity of the uniform attractors {Aε} ε∈[0,1] at ε = 0 is also studied.

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We consider for \rho \in [0,1) and \varepsilon > 0 , the following nonclassical diffusion equations with memory and singularly oscillating external force u_t -\Delta u_t - \Delta u - \int_0^\infty \kappa (s) \Delta u(t-s)ds+ f(u) = g_0(t)+\varepsilon^{- \rho}g_1(t/\varepsilon), together with the averaged equation u_t - \Delta u_t - \Delta u - \int_0^\infty \kappa (s) \Delta u(t-s)ds+ f( u) = g_{0}( t) formally corresponding to the limiting case \varepsilon=0 . Under suitable assumptions on the nonlinearity and on the external force, we prove the uniform (w.r.t. \varepsilon ) boundedness as well as the convergence of the uniform attractor \mathcal A^{\varepsilon} of the first equation to the uniform attractor \mathcal A^{0} of the second equation as \varepsilon \to 0^+ .