The paper is devoted to establishing strong consistency of estimates of nonlinear characteristics of dynamic stochastic systems. To describe the shape of the nonlinearities, regression functions, i.e. conditional expectations of a random variable with respect to another one, are used. In turn, the nonlinear regression functions are estimated by using kernel-type algorithm approaches, which are suitable under fairly mild assumptions with respect to the system description. Within the approach, the key issue of the present paper is considering a case of mutually dependent observations. At the same time, conventional nonparametric approaches are based on regression estimates, which impose a number of conditions on sampled data, e.g. mutual independence, various mixing conditions, etc., while such assumptions are not always suitable for verifying within the practice of dynamic system considerations.