Consideration was given to the method of statistical linearization of nonlinear stochastic plants on the basis of the dispersion identification theory for the Hammerstein class of models. The problem is notable for taking into account the dynamic nonlinearities of the plant. Models of statistical linearization were constructed with regard for the plant output noise of the kind of white noise and martingale sequence. Solution was obtained in the class of gradient recurrent identification algorithms. The necessary and sufficient conditions for strong consistency of the parameter estimates provided by these algorithms were presented. The results obtained were used for adaptive following of the plant output. Fitness of this method was substantiated by the example of a particular plant.