Present thesis is devoted to symbolical discretization of nonlinear continuous-time systems and application of a class of neural networks based discrete-time models to control of nonlinear systems. The first part of this thesis concentrates its attention on discretization theory of continuous time systems and especially on the theory of so called finitely discretizable systems. Besides that, the author considers the implementation of the functions on the basis of the presented theory in Computer Algebra System (CAS) Mathematica. The second part of this thesis is devoted to the application of Neural Networks based Additive Nonlinear Autoregressive eXogenous (NN-based ANARX) structure to identification and control of nonlinear systems. The advantage of using this structure lies in the fact that it is always linearizable by dynamic output feedback as well as representable in a classical state-space form. Different approaches for calculation of control signals by using NN-ANARX based dynamic output linearization algorithm are also considered. The effectiveness of presented techniques is demonstrated on numerical examples. All calculations and simulations shown in this thesis are performed in Mathematica and MATLAB/Simulink environments.