A key to overcoming the limitations of classical artificial intelligence and to deal well with enormous amounts of information might be brain-like computing in which distributed representations of information are processed by dynamical systems without using symbols. We present a method for such computing. We constructed an inference system using a nonmonotone neural network, which is a kind of recurrent neural network with continuous-time dynamics. This system deduces a conclusion according to state transitions of the network in which knowledge is embedded as trajectory attractors. It has the powerful ability of analogical reasoning without special treatment for exceptional knowledge. We also propose a method of linking different neurodynamical systems and show that two mutually interacting systems can process complex spatiotemporal patterns. Keywords Distributed Representations, Neurodynamics, Nonmonotone Neural Network, Selective Desensitization, Brain-like Information Processing.