The response of the gill of Aplysia calfornica Cooper to weak to moderate tactile stimulation of the siphon, the gill-withdrawal response or GWR, has been an important model system for work aimed at understanding the relationship between neural plasticity and simple forms of non-associative and associative learning. Interest in the GWR has been based largely on the hypothesis that the response could be explained adequately by parallel monosynaptic reflex arcs between six parietovisceral ganglion (PVG) gill motor neurons (GMNs) and a cluster of sensory neurons termed the LE cluster. This hypothesis, the Kupfermann-Kandel model, made clear, falsifiable predictions that have stimulated experimental work for many years. Here, we review tests of three predictions of the Kupfermann-Kandel model: (1) that the GWR is a simple, reflexive behaviour graded with stimulus intensity; (2) that central nervous system (CNS) pathways are necessary and sufficient for the GWR; and (3) that activity in six identified GMNs is sufficient to account for the GWR. The available data suggest that (1) a variety of action patterns occur in the context of the GWR; (2) the PVG is not necessary and the diffuse peripheral nervous system (PNS) is sufficient to mediate these action patterns; and (3) the role of any individual GMN in the behaviour varies. Both the control of gill-withdrawal responses, and plasticity in these responses, are broadly distributed across both PNS and CNS pathways. The Kupfermann-Kandel model is inconsistent with the available data and therefore stands rejected. There is, no known causal connection or correlation between the observed plasticity at the identified synapses in this system and behavioural changes during non-associative and associative learning paradigms. Critical examination of these well-studied central pathways suggests that they represent a 'wetware' neural network, architecturally similar to the neural network models of the widely used 'Perceptron' and/or 'Back-propagation' type. Such models may offer a more biologically realistic representation of nervous system organisation than has been thought. In this model, the six parallel GMNs of the CNS correspond to a hidden layer within one module of the gill-control system. That is, the gill-control system appears to be organised as a distributed system with several parallel modules, some of which are neural networks in their own right. A new model is presented here which predicts that the six GMNs serve as components of a 'push-pull' gain control system, along with known but largely unidentified inhibitory motor neurons from the PVG. This 'push-pull' gain control system sets the responsiveness of the peripheral gill motor system. Neither causal nor correlational links between specific forms of neural plasticity and behavioural plasticity have been demonstrated in the GWR model system. However, the GWR model system does provide an opportunity to observe and describe directly the physiological and biochemical mechanisms of distributed representation and parallel processing in a largely identifiable 'wetware' neural network.