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We have obtained the sufficient conditions for identifiability of the mathematical models of evolutionary processes, which are linear in estimated parameters, by using restricted samples of data of the discrete indirect measurements of their state vectors, given the incomplete a priori deterministic information concerning the initial (boundary) conditions.When solving the problems on parametric identification of the mathematical models for different evolutionary processes we use the results of a limited number of indirect measurements of their state vectors [2][3][4]9]. The sufficient conditions for solving the parametric identification problems of this class were obtained in [10]. However, there is a broad class of problems on parametric identification of the mathematical models for evolutionary processes in which we use, as initial data, deterministic and generally incomplete a priori information concerning the initial (boundary) conditions along with the results of a limited number of discrete indirect measurements of the state vector [2,3,17].The aim of our research is to study the statistical solvability of the problems on parametric identification of the mathematical models for any evolutionary processes by using restricted samples of data of the discrete indirect measurements of their state vectors, given the incomplete a priori deterministic information concerning the initial (boundary) conditions.