The functional significance of changes in the size of the afterhyperpolarization, observed in a range of neural contexts, has not been well characterized. Features of the slow afterhyperpolarization, driven by gK + (Ca), were accordingly incorporated into the elements of a densely connected, artificial neural network with a known computational function (autoassociation). The connections among its elements were specified so that the network without these features would respond to a stimulus with a sustained stimulus-specific spatial pattern of spiking. Large magnitudes of gK + (Ca) destablized these stimulus-specific equilibria. Increases in the transmission delay between elements or in synaptic duration, however, preserved the stimulus-specific outputs of the networks at a corresponding magnitude of gK + (Ca). These simulations may have application to a broad range of topics: the timing of network outputs, accentuation of synaptic plasticity, roles for slow synaptic conductances and neuromodulation, and the selection of different outputs from networks with fixed connectivities.