Gnathonemus petersii, a pulse-emitting African species of weakly electric fish, locates objects in its environment by measuring distortions of its own electric organ discharge at cutaneous electroreceptors (Bell, 1989). It is hypothesized that current intensity at these mormyromast electroreceptors is neurally represented as the latency with which mormyromast afferent fibers generate action potentials, and that this latency is decoded by a corollary discharge mechanism (Szabo and Hagiwara, 1967) at the granular cell layer of the electrosensory lateral line lobe. Extracellular recordings from these granular cells (Bell and Grant, 1992), along with intracellular recordings from afferent fibers that are electrotonically coupled to granular cells (Bell and Grant, 1992), are used in this study as the basis of a mathematical model of granular cell responsiveness in the NEURON simulation environment (Hines and Carnevale, 1997). The model shows that the cooperative effects of a persistent Na+ current (I-NaP) and slow repolarizing K+ current (I-KM) are sufficient to explain control of burst onset latency in granular cells. Control of burst offset latency is predicted by the model to be controlled either by GABAergic inhibition from large multipolar interneurons of the electrosensory lateral line lobe or by variations in the activation gating kinetics of I-KM. The temporal precision of granular cell responsiveness is shown to require either that (1) both the juxtalobar and primary afferent inputs contain electrical, gap junction mediated inputs or that (2) the glutamatergic components of each input are almost entirely driven by AMPA-R activation. Furthermore, transformation of the latency code for stimulus intensity in afferent fibers to a burst duration code in the model granular cell was shown to be relatively robust under moderate perturbation of current densities. This supports the biological plausibility of the burst duration (or spike number) code, especially under conditions of granular cell response pooling and coregulation of I-NaP and I-KM currents.