Journal article: 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 with 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 λ-discounted games and that it coincides with the value of the continuous time game.