In this paper we provide generalizations of Zubov's equation to differential games without the Isaacs condition. We show that both generalizations of Zubov's equation (which we call the min-max and max-min Zubov equation, respectively) possess unique viscosity solutions which characterize the respective controllability domains. As a consequence, we show that under the usual Isaacs condition the respective controllability domains as well as the local controllability assumptions coincide.