In this paper the theory of the electrophoretic mobility and electrical conductivity of concentrated suspensions of spherical colloidal particles, developed by H. Ohshima (J. Colloid Interface Sci. 188, 481 (1997); J. Colloid Interface Sci. 212, 443 (1999)), has been revised and extended to include the effect of a dynamic Stern layer on the surface of the particles. The starting point has been the theory developed by C. S. Mangelsdorf and L. R. White (J. Chem. Soc., Faraday Trans. 86, 2859 (1990)) dealing with the calculation of the electrophoretic mobility of a colloidal particle, when lateral motion of ions in the inner region of the double layer is possible (dynamic Stern layer (DSL)). The effects of Stern layer parameters on the electrophoretic mobility are first discussed and compared with the case when a Stern layer is,absent. The numerical results show that regardless of the values of the Stern layer and solution parameters chosen, the presence of a DSL causes the electrophoretic mobility to decrease in comparison with the standard case (no Stern layer present) for every volume fraction. Furthermore, the stronger the hydrodynamic particle-particle interactions as volume fraction increases, the lower the mobility for a given zeta potential, both mechanisms tending to increase the retarding forces that brake the electrophoretic motion. Concerning direct current conductivity calculations, results show that the presence of a DSL causes the electrical conductivity to increase in comparison with the standard case (no Stern layer present) for every volume fraction and zeta potential. Obviously, the additional conductivity contribution of every particle in the system is related to the presence of an extra mobile layer, the DSL. The treatment is based on the use of a cell model to account for hydrodynamic and electrical interactions between particles. We also discuss the use of either Levine-Neale or Shilov-Zharkikh boundary conditions, leading to different results for the mobility and direct current conductivity in conditions of both low (where analytical expressions can be reached) and arbitrary zeta potentials. The analogies and discrepancies between both approaches are discussed.