The overall objective of this project is to develop a set of well definedperformance indices and evaluation techniques to replace many ad-hoc cut-and-try efforts currently used in neural network design. This project is a studyof the state space of two neural networks: the asynchronous binary neural network (ABNN), and the Adaptive Resonance Theoretic model (ART1). The project concentrates on the adaptation of these two structures to realistic pattern environments, which are short-term but not long term stationary. Specific goals include the analysis of the dynamic behavior in the model's state space, and the introduction of structural and algorithmic modifications that will improve their performance as pattern recognizers. An analytical approach based on Markov chain theory, branching processes, and optimal stopping rules will be used. The analysis will be verified through simulations on a serial computer as well as a truly parallel implementation on an analog computer.