Path integrals for a nonadditive action

The path integral for the case of nonadditive action appeared in the some problems of solid state physics and problems concerning the propagation of the radiation in the random media is considered. The complimentary difficults in compare with the case of additive action are discussed. For the treated Green function the Dyson type integral equation in which vertex function is represented as the series of perturbation theory is derived. In the one special case the exact solution is recieved and the nonunit arity of this solution is discussed.