  In this paper, we investigate the mean field games with $K$ classes of agents
who are weakly coupled via the empirical measure. The underlying dynamics of
the representative agents is assumed to be a controlled nonlinear Markov
process associated with rather general integro-differential generators of
L\'evy-Khintchine type (with variable coefficients). We show that nonlinear
measure-valued kinetic equations describing the dynamic law of large numbers
limit for system with large number N of agents are solvable and that their
solutions represent 1/N-Nash equilibria for approximating systems of N agents.
