The conductance of ionic species through a cylindrical nanochannel is explored by means of a mesoscopic lattice Boltzmann numerical method. It is shown that in the absence of any external voltage, the ionic profiles develop a considerable amount of structure within the channel. The details of this structure depend on the ionic density, channel length, and Debye length. In the presence of a trans-membrane electrostatic potential, less structure is observed and Ohm's law is found to hold. (C) 2004 American Institute of Physics.