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Cooperative and competitive computations seem to play a greater role in decision making in neural circuitry than do execu—tive controls. A number of neural models have been proposed which include cooperative and competitive computations——eg, the model of the role of the reticular formation in deciding the overall mode of behavior, the model of how the frog's tectum decides the snapping position, and the model of the use of stereopsis to rec—ognize depth in space. The aim of this paper is to develop a mathematical study of these models (especially the latter two) as a theory of neural fields. Special attention is given to the analysis of equilibrium states of the system and their stability, and to the interaction of different stimuli separated in space and time.