This article is concerned with an artificial neural system for a mobile robot reactive navigation in an unknown, cluttered environment. Reactive navigation is a process of immediately choosing locomotion actions in response to measured spatial situations, while no planning occurs. A task of a presented system is to provide a steering angle signal letting a robot reach a goal while avoiding collisions with obstacles. Basic reactive navigation methods are briefly characterized, special attention is paid to a neural approach to the considered problem. The authors describe the system's architecture and important details of the algorithm. The main parts of the system are: the Fuzzy ART neural self-organizing classifier, performing a perceptual space partitioning, and a neural associative memory, memorizing the system's experience and superposing influences of different behaviors. Tests show that the learning process, starting from zero, is efficient, despite some initial fluctuations of its effectiveness.