We consider two person zero-sum games where the players control at discrete times of a partition  a continuous time  Markov   process. 
We prove that the limit of the values of the game exist as the mesh goes to 0.
The analysis covers  the cases of:

1)   stochastic games (where both players know the state)

2)   symmetric no  information case.

 The proof is by reduction to  deterministic differential games.