  Given $\rho\in[0,1]$, we consider for $\varepsilon\in(0,1]$ the nonautonomous
viscoelastic equation with a singularly oscillating external force $$
\partial_{tt} u-\kappa(0)\Delta u - \int_0^\infty \kappa'(s)\Delta u(t-s) d s
+f(u)=g_{0}(t)+\varepsilon ^{-\rho }g_{1}(t/\varepsilon ) $$ together with the
{\it averaged} equation $$ \partial_{tt} u-\kappa(0)\Delta u - \int_0^\infty
\kappa'(s)\Delta u(t-s) d s +f(u)=g_{0}(t). $$ Under suitable assumptions on
the nonlinearity and on the external force, the related solution processes
$S_\varepsilon(t,\tau)$ acting on the natural weak energy space ${\mathcal H}$
are shown to possess uniform attractors ${\mathcal A}^\varepsilon$. Within the
further assumption $\rho<1$, the family ${\mathcal A}^\varepsilon$ turns out to
be bounded in ${\mathcal H}$, uniformly with respect to $\varepsilon\in[0,1]$.
The convergence of the attractors ${\mathcal A}^\varepsilon$ to the attractor
${\mathcal A}^0$ of the averaged equation as $\varepsilon\to 0$ is also
established.
