  In this paper we consider the homogenization problem for a nonlocal equation
that involve different smooth kernels. We assume that the spacial domain is
divided into a sequence of two subdomains $A_n \cup B_n$ and we have three
different smooth kernels, one that controls the jumps from $A_n$ to $A_n$, a
second one that controls the jumps from $B_n$ to $B_n$ and the third one that
governs the interactions between $A_n$ and $B_n$.
  Assuming that $\chi_{A_n} (x) \to X(x)$ weakly-* in $L^\infty$ (and then
$\chi_{B_n} (x) \to (1-X)(x)$ weakly-* in $L^\infty$) as $n \to \infty$ we show
that there is an homogenized limit system in which the three kernels and the
limit function $X$ appear.
  We deal with both Neumann and Dirichlet boundary conditions. Moreover, we
also provide a probabilistic interpretation of our results.
