  We prove a compactness result with respect to $\Gamma$-convergence for a
class of integral functionals which are expressed as a sum of a local and a
non-local term. The main feature is that, under our hypotheses, the local part
of the $\Gamma$-limit depends on the interaction between the local and
non-local terms of the converging subsequence. The result is applied to
concentration and homogenization problems.
