Several observations suggest that the Ca2(+)-dependent postsynaptic release of nitric oxide (NO) may be important in the formation and function of the vertebrate nervous system. We explore here the hypothesis that the release of NO and its subsequent diffusion may be critically related to three aspects of nervous system function: (i) synaptic plasticity and long-term potentiation in certain regions of the adult nervous system, (ii) the control of cerebral blood flow in such regions, and (iii) the establishment and activity-dependent refinement of axonal projections during the later stages of development. In this paper, we detail and analyze the basic assumptions underlying this NO hypothesis and describe a computer simulation of a minimal version of the hypothesis. In the simulation, a 3-dimensional volume of neuropil is presented with patterned afferent input; NO is produced, diffuses, and is destroyed; and synaptic strengths are determined by a set of synaptic rules based on the correlation of synaptic depolarization and NO levels. According to the hypothesis, voltage-dependent postsynaptic release of this rapidly diffusing substance links the activities of neurons in a local volume of tissue, regardless of whether the neurons are directly connected by synapses. This property is demonstrated in the simulation, and it is this property that is exploited in the hypothesis to account for certain aspects of long-term potentiation and activity-dependent sharpening of axonal arbors.