  We discuss $G$-convergence of linear integro-differential-algebaric equations
in Hilbert spaces. We show under which assumptions it is generic for the limit
equation to exhibit memory effects. Moreover, we investigate which classes of
equations are closed under the process of $G$-convergence. The results have
applications to the theory of homogenization. As an example we treat Maxwell's
equation with the Drude-Born-Fedorov constitutive relation.
