  We study the asymptotic value of a frequency-dependent zero-sum game with
separable payoff following a differential approach. The stage payoffs in such
games depend on the current actions and on a linear function of the frequency
of actions played so far. We associate to the repeated game, in a natural way,
a differential game and although the latter presents an irregularity at the
origin, we prove that it has a value. We conclude, using appropriate
approximations, that the asymptotic value of the original game exists in both
the n-stage and the {\lambda}-discounted games and that it coincides with the
value of the continuous time game.
