The aim of the paper is to present a general approach to the identification of nonlinear stochastic systems based on information-theoretic measures of dependence. In the paper, an identification problem statement using an information-theoretic criterion under rather general conditions is proposed. It is based on a parameterized description of the model of a system under study combined with a corresponding method of estimation of the mutual information of the system and model output variables. Such a problem statement leads finally to a problem of the finite dimensional optimization. As a result, a constructive procedure of the model parameter identification is derived. It possesses a high level of generality and does not involve unrealistic a priori assumptions that degenerate the entity of the initial identification problem statement like those ones presented in some referenced literature sources and revised in the present paper.