Neural networks have been found to be useful as a technique for the modeling of non-linear functions or processes that involve several variables. The primary goal of this thesis is to explore the feasibility of applying feedforward backpropagation neural networks in the optimization of multistage thermal systems. Basically, the idea consists of using neural networks as a function approximation technique for each stage of a multistage process. After the successful approximation, existing optimization methods are used to obtain the parameters that optimize the system. In addition, it is shown how feedforward backpropagation neural networks can be used in solving calculus of variation problems, by separating the process into discrete stages, thus forming a multistage process problem. Finally, parallel work was done in developing a faster deterministic training algorithm, as an alternative to the time consuming backpropagation training algorithm.