The recent finding that dendritic spines (on which 90 per cent of all excitatory synapses on pyramidal cells are formed) are not permanent structures but are continually being formed and adsorbed has implications for the present theoretical basis of neurocomputation, which is largely based on the concept of fixed nerve nets. This evidence would tend to support the recent theories of Edelman, Freeman, Globus, Pribram and others that neuronal networks in the brain operate mainly as nonlinear dynamic, chaotic systems. This paper presents a hypothesis of a possible neurochemical mechanism underlying this synaptic plasticity based on reactive oxygen species and toxic o–semiquinones derived from catecholamines (i) by the enzyme prostaglandin H synthetase induced by glutamatergic NMDA receptor activation and (ii) by reactive nitrogen species derived from nitric oxide in a low ascorbate environment. A key factor in this neuromodulation may be the fact that catecholamines are potent antioxidants and free radical scavengers and are thus able to affect the redox mediated balance at the glutamate receptors between synapse formation and synapse removal that may be a key factor in neurocomputational plasticity. But catecholamines are also easily oxidized to neurotoxic o–semiquinones and this may be relevant to the pathology of several diseases including schizophrenia. The relationship between dopamine release and positive reinforcement is relevant to this hypothesis.