The myelin sheath is normally regarded as an electrical insulator. Low values of radial conductance and capacitance have been measured, and in electrical models of myelinated axons the contribution of longitudinal conduction within the sheath has been ignored. According to X-ray diffraction studies, however, myelin sheaths comprise alternate lipid and aqueous layers, and the latter may be expected to have a low resistivity. We propose a new model of myelinated axons in which the aqueous layers within the myelin provide appreciable longitudinal and radial conductance, the latter via a spiral pathway. We have investigated the likely contribution of these conductive paths within the myelin to the electrical properties of a human motor nerve fibre by computer simulation, representing the myelin sheath as a series of interconnecting parallel lamellae. With this new model, action potential conduction has been simulated along a 20-node cable, and the electrotonic responses to 100-ms depolarizing and hyperpolarizing current pulses have been simulated for a uniformly polarized fibre. We have found that the hypothesis of a longitudinally conducting myelin sheath improves our previous model in two ways: it is no longer necessary to make implausible assumptions about the resistivity or width of the periaxonal space to simulate realistic electrotonus, and the conduction velocity is appreciably faster (by 8.6%).