We address the problem of existence of the uniform value in recursive games. We give two existence results. (i) The uniform value is shown to exist if the state space is countable, the action sets are finite and if, for some a > 0, there are finitely many states in which the limsup value is less than a. (ii) For games with non-negative payoff function, it is sufficient that the action set of player 2 is finite. The finiteness assumption can be further weakened.