  A system of $N$ weakly interacting particles whose dynamics is given in terms
of jump-diffusions with a common factor is considered. The common factor is
described through another jump-diffusion and the coefficients of the evolution
equation for each particle depend, in addition to its own state value, on the
empirical measure of the states of the $N$ particles and the common factor. A
Central Limit Theorem, as $N \to \infty$, is established. The limit law is
described in terms of a certain Gaussian mixture. An application to models in
Mathematical Finance of self-excited correlated defaults is described.
