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Intrinsic sensory neurons of the intestine are connected together to form a recurrent network. They interact by slow excitatory post synaptic potentials (EPSPs), which have a complex dependence on the pattern of input. These networks are unstable and unable to give graded responses to sensory input without some form of inhibition, but inhibitory synaptic potentials are rare in this system. Intrinsic sensory neurons have a characteristic after-hyperpolarization (AHP), but this is depressed during slow EPSPs. To test whether AHPs can provide the inhibition necessary for stability, AHPs, slow EPSPs and their interactions were included in a computer simulation of realistic sensory neuron networks. Residual AHPs as small as 1% of control were found to lead to stable networks capable of giving graded responses.