The reseach on neural networks has been done for six decades. In this period, many neural models and learning rules have been proposed. Futhermore, they were popularly and successfully applied to many applications. They successfully solved many problems that traditional algorithms could not solve efficiently . However, applying multilayer neural networks to applications, users are confronted with the problem of determining the number of hidden layers and the number of hidden neurons in each hidden layer. It is too difficult for users to determine proper neural network architectures. However, it is very significant, because neural network architectures always influence critically their performance. We may solve problems efficiently, only when we has proper neural network architectures. To overcome this difficulty, several approaches have been proposed to generate the architecture of neural networks recently. However, they still have some drawbacks. The goal of our research is to discover better approachs to automatically determine proper neural network architectures. We propose a series of approaches in this thesis. First, we propose an approach based on decision trees. It successfully determines neural network architectures and greatly decreases learning time. However, it can deal only with two-class problems and it generates bigger neural network architectures. Next, we propose an information entropy based approach to overcome the above drawbacks. It can generate easily multi-class neural networks for standard domain problems. Finally, we expand the above method for sequential domain and structured domain problems. Therefore, our approaches can be applied to many applications. Currently, we are trying to work on quantum neural networks. We are also interested in ART neural networks. They are also incremental neural models. We apply them to digital signal processing. We propose a character recognition application, a spoken word recognition application, and an image compression application. All of them have good performances.