An approach concerned with issues of applying consistent measures of dependence within stochastic non-linear system identification is presented. A measure of dependence of a pair of random values is referred as consistent, if it vanishes if and only if these random values are stochastically independent. Finally, the approach is oriented to the elimination of drawbacks concerned with applying conventional, based on the linear correlation measures of dependence. Within the approach proposed, a technique of deriving measure of dependence meeting the Rényi Axioms is derived; specific forms of consistent measures of dependence based on the Rényi entropy are proposed.