A theory is proposed for the dynamic electrophoretic mobility mu(omega) of spherical colloidal particles in a salt-free medium containing only counterions in an oscillating electric field of frequency omega. The dynamic mobility depends on the frequency omega of the applied electric field and on the particle volume fraction as well as on the particle surface charge. It is found that as in the case of the static electrophoretic mobility mu(0) in salt-free media, there is a certain critical value of the particle surface charge separating two cases, that is, the low-surface-charge case and the high-surface-charge case (in the latter case the counterion condensation takes place near the particle surface). For the low-surface-charge case, the dynamic mobility agrees with that of a sphere in an electrolyte solution in the limit of very low electrolyte concentrations kappaa --> 0 (Huckel's limit), where kappa is the Debye-Huckel parameter and a is the particle radius. For the high-surface-charge case, however, the dynamic mobility becomes constant independent of the particle surface charge, because of the counterion condensation effects. A simple expression for the ratio mu(omega)/mu(0) applicable for all cases is given. (C) 2003 Elsevier Inc. All rights reserved.