The slow depolarization that underlies the voltage-dependent burst-firing behavior of human neocortical neurons is mediated by a low-threshold calcium conductance in concert with the anomalous rectifier current, Ih. The slow depolarization could be elicited by depolarization from negative membrane potentials or as a rebound following hyperpolarization. The rebound depolarization was time- and voltage-dependent. Most of the slow depolarization was blocked by inorganic calcium blockers. The remainder of the depolarization and the 'sag' in the hyperpolarizing voltage responses were blocked by extracellular Cs+.