1. Individual leech Retzius (Rz) cells were removed from mid-body ganglia and plated in cell culture on concanavalin A or polylysine. Experiments on the majority of cells were performed after 6-11 days in culture. Isolated Rz cells were superfused with normal leech saline (NS), cobalt saline (Ca2+ replaced with Co2+), or one of a variety of other modified salines. 2. Prolonged plateau potentials (PPs) with durations ranging from several seconds to nearly 2 min were evoked in isolated Rz cells in response to 1-s depolarizing current pulses delivered under discontinuous current clamp. Some PPs terminated spontaneously while others were terminated with hyperpolarizing current pulses. PPs were associated with a dramatic increase in the input conductance of the neuron. The PP decayed slightly over time, and this decay was accompanied by a small decrease in the input conductance. 3. PP duration was enhanced by penetrating cells with electrodes containing tetraethylammonium (TEA) and by bathing cells in Co2+ saline, but PPs were evoked also in NS and using electrodes without TEA. The effects of TEA and Co2+ saline suggest that voltage-dependent and especially calcium-dependent outward currents normally suppress plateau formation. 4. PPs occurred most reliably in neurons with extensive neurite sprouting. Isolated somata with few or no neurites usually failed to express PP, although there were several exceptions to this trend. 5. PPs persisted when Ca2+ was replaced with either of the calcium channel blockers Co2+, Ni2+, or Mn2+, when 200 microM Cd2+ was added to normal saline, or when Na+ was replaced with Li+. In contrast, PPs were eliminated rapidly when Na+ was replaced with N-methyl-D-glucamine. 6. Isolated Rz cells also expressed repetitive PPs either spontaneously or in response to injection of sustained depolarizing current. Spontaneous repetitive PPs were suppressed by hyperpolarizing current. Repetitive PPs in isolated Rz cells are similar in many respects to the bursting electrical activity induced by Co2+ saline in Rz and other neurons in intact ganglia. 7. The ionic dependence and prolonged duration of PPs suggest that these responses are generated by a persistent voltage-dependent Na+ current. A quantitative computer simulation of PPs was achieved using a depolarization-activated Na+ conductance with very slow inactivation. Repetitive PPs were simulated by addition of a slow outward current in the form of an electrogenic pump.