Summary: In the present work, we consider 2-person zero-sum stochastic differential games with a nonlinear pay-off functional which is defined through a backward stochastic differential equation. Our main objective is to study the problem of the existence of a value without Isaacs condition. Not surprising, this requires a suitable concept of mixed strategies which, to the authors’ best knowledge, was not known in the context of stochastic differential games. For this, we consider nonanticipative strategies with a delay defined through a partition \(\pi\) of the time interval \([0,T]\). The underlying stochastic controls for both players are randomized along \(\pi\) by a hazard which is independent of the governing Brownian motion, and knowing the information available at the left time point \(t_{j-1}\) of the subintervals generated by \(\pi\), the controls of players 1 and 2 are conditionally independent over \([t_{j-1},t_{j})\). It is shown that the associated lower and upper value functions \(W^{\pi}\) and \(U^{\pi}\) converge uniformly on compacts to a function \(V\), the so-called value in mixed strategies, as the mesh of \(\pi\) tends to zero. This function \(V\) is characterized as the unique viscosity solution of the associated Hamilton-Jacobi-Bellman-Isaacs equation.