The first part of this paper reviews the theory of the calculation of the frequency-dependent dielectric properties (i.e., conductivity and dielectric constant) of ionic solutions from computer simulations. Based on a 2.2-ns molecular dynamics simulation, the second part presents a detailed analysis of the various contributions to the frequency-dependent conductivity of a saturated solution of ZnBr2 in water. We find evidence for two separate relaxation channels in the frequency-dependent conductivity, and a very low value for the static (i.e., zero frequency) conductivity, which is consistent with the high degree of ion association and the prevalence of electrically neutral ion clusters that we observe in this system. (C) 1997 American Institute of Physics.