The final work of A.S. Shekhovtsov is devoted to the analysis of the dynamics of the solutions of the model equation of nuclear decay as a function of the coefficients of the equation and taking into account delayed neutrons. The nominal system is described by a linear differential equation of a delayed or neutral type, depending on which factor of the real process is the most determinant. The problem considered by the author is relevant, since controlled dynamic systems that take into account the transport delay in the feedback channel, and in this process the delay factor is due to the presence of secondary and tertiary neutrons, and other factors of possible uncertainty of the system being simulated, are a more adequate tool for mathematical modeling of the dynamics of technical objects and Technological processes. In this paper A.S. Shekhovtsov had time to consider only one equation with one lag type delay concentrated type and one neutral type equation. A.S. Shekhovtsov used the D-decomposition method to analyze the robust stability of a nominal equation and the Lyapunov-Krasovskii method for analyzing the initial nonlinear and non-stationary equations as a method of investigating stability. Unfortunately, until the end of the second part of the work was not brought. The graduation qualification work consists of an introduction in which mathematical models of the considered nuclear decay equations are justified, problems are formulated and a review of the literature, two chapters containing the results of the work and an example, conclusions and a list of used literature is done. In the introduction and the section "Statement of the problem", the relevance of the task is justified. Also here the main purpose of the thesis is formulated. The first chapter outlines the basic concepts of the theory of ordinary differential and differential-difference equations and the D-decomposition method for analyzing the stability of a nominal equation. In the second chapter the author describes the method of constructing the Lyapunov-Krasovskii functional and, for the considered nuclear decay equation, carries out the necessary calculations. We note that although the results obtained by A.S. Shekhovtsov refer to a scalar equation, they can easily be transferred to the case of a system of equations. After that, it will be possible to compare the results of numerical simulation with the observed data of the real process and draw a conclusion about the adequacy of the constructed mathematical model. When working on WRC student A.Shekhovtsov showed sufficient independence. He studied and modernized the necessary algorithms, showed the necessary perseverance in overcoming the mathematical difficulties encountered during the work and demonstrated the knowledge acquired during the training at the university. Considering the foregoing, I consider that the final qualification work of Anton Sergeevich Shekhovtsov "Analysis of the stability of the nuclear decay equation with allowance for delayed neutrons" corresponds to the direction "Applied Mathematics and Physics" and deserves an "excellent" evaluation.