The theory developed by O'Brien and White (R. W. O'Brien and L. R. White, J. Chem. Soc., Faraday Trans. 2, 1978, 77, 1607) to calculate the electrophoretic mobility of a solid, spherical colloidal particle, is reviewed and extended. The equations governing the ion distribution, electrostatic potential and hydrodynamic flow field around the particle, are modified to allow for the lateral movement of ions within the Stern layer. Two classes of Stern-layer adsorption isotherms are considered: (1) adsorption of ions onto available surface area; (2) adsorption of ions onto underlying surface charge (C. F. Zukoski IV and D. A. Saville, J. Colloid Interface Sci., 1986, 114, 32). The model equations are solved numerically for both adsorption isotherms, and the effects of varying individual Stern-layer parameters on the electrophoretic mobility and conductivity increment, are discussed and compared with the case when surface conductance is absent. Regardless of the adsorption model used, the presence of mobile Stern-layer ions causes the mobility to decrease and the conductivity to increase, in comparison with the case when surface conduction is absent. The magnitude of this effect is greater in model (2) owing to important contributions from both coion and counterion adsorption. Furthermore extra conditions on the surface charge density in model (2) can lead to negative site densities for some positive zeta potentials and ridiculously high site densities at large zeta or high salt concentrations. In contrast, model (1) shows negligible coion adsorption and modest charge densities throughout the range of zeta and salt concentration. A program for calculating electrokinetic transport properties, including these models of Stern-layer transport, is available from the authors.