We first model and analyze distributed systems including distributed sensors and actuators. We then consider identification of distributed systems via adaptive wavelet neural networks (AWNNs) by taking advantage of the multiresolution property of wavelet transforms and the parallel computational structure of neural networks. A new systematic approach is developed in this dissertation to construct an optimal discrete orthonormal wavelet basis with compact support for spanning the subspaces employed for system identification and signal representation. We then apply a backpropagation algorithm to train the network to approximate the system. Filter banks for parameterizing wavelet systems are studied. An analog VLSI implementation architecture of the AWNN is also given in this dissertation. This work is applicable to signal representation and compression under optimal orthonormal wavelet bases in addition to progressive system identification and modeling. We anticipate that this work will find future applications in signal processing and intelligent systems.