For a highly charged particle in an electrolyte solution, counterions are condensed very near the particle surface. The electrochemical potential of counterions accumulated near the particle surface is thus not affected by the applied electric field, so that the condensed counterions do not contribute to the particle electrophoretic mobility. In the present paper we derive an expression for the electrophoretic mobility mu(infinity) of a highly charged spherical particle of radius a and zeta potential zeta in the limit of very high zeta in a solution of general electrolytes with large Ka (where K is the Debye-Huckel parameter) on the basis of our previous theory for the case of symmetrical electrolytes (H. Ohshima, J. Colloid Interface Sci. 263 (2003) 337). It is shown that zeta can formally be expressed as the sum of two components: the co-ion component, co-ion, and the counterion component, zeta(counterion) (where zeta = zeta(co-ion) + zeta(counterion)) and that the limiting electrophoretic mobility mu(infinity) is given by mu(infinity) = epsilon(r)epsilon0(r)zeta(co-ion)(infinity)/eta + O (1/Ka), where zeta(co-ion)(infinity) is the high zeta-limiting form of zeta(-co-ion), epsilon(r) and eta are, respectively, the relative permittivity and viscosity of the solution, and so is the permittivity of a vacuum. That is, the particle behaves as if its zeta potential were zeta(co-ion) independent of zeta. For the case of a positively charged particle in an aqueous electrolyte solution at 25 degreesC, the value of zeta(co-ion)(infinity) is 35.6 mV for l(-1) electrolytes, 46.0 mV for 2-1 electrolytes, and 12.2 mV for 1-2 electrolytes. It is also found that the magnitude of mu(infinity) increases as the valence of co-ions increases, whereas the magnitude of mu(infinity) decreases as the valence of counterions increases. (C) 2004 Elsevier Inc. All rights reserved.