The rhythmic pyloric network of the lobster stomatogastric system approximately maintains phase (that is, the burst durations and durations between the bursts of its neurons change proportionally) when network cycle period is altered by current injection into the network pacemaker (Hooper, 1997a,b). When isolated from the network and driven by rhythmic hyperpolarizing current pulses, the delay to firing after each pulse of at least one network neuron type [pyloric (PY)] varies in a phase-maintaining manner when cycle period is varied (Hooper, 1998). These variations require PY neurons to have intrinsic mechanisms that respond to changes in neuron activity on time scales at least as long as 2 s. Slowly activating and deactivating conductances could provide such a mechanism. We tested this possibility by building models containing various slow conductances. This work showed that such conductances could indeed support intrinsic phase maintenance, and we show here results for one such conductance, a slow potassium conductance. These conductances supported phase maintenance because their mean activation level changed, hence altering neuron postinhibition firing delay, when the rhythmic input to the neuron changed. Switching the sign of the dependence of slow-conductance activation and deactivation on membrane potential resulted in neuron delays switching to change in an anti-phase-maintaining manner. These data suggest that slow conductances or similar slow processes such as changes in intracellular Ca(2+) concentration could underlie phase maintenance in pyloric network neurons.