A theory is proposed for the electrophoretic mobility mu of dilute spherical liquid drops of radius a in salt-free media containing only counterions (e.g., nonaqueous media). As in the case of the electrophoretic mobility of rigid particle in salt-free media, there is a certain critical value of the drop surface charge separating two cases, that is, the low-surface-charge case and the high-surface-charge case. For the low-surface-charge case, mu coincides with that of a drop in an electrolyte solution in the limit of very low electrolyte concentrations kappaa --> 0 (Huckel's limit), where kappa is the Debye-Huckel parameter. For the high-surface-charge case, however, mu becomes constant independent of the drop surface charge, since the counterion condensation takes place near the drop surface. (C) 2003 Elsevier Science (USA). All rights reserved.