The motion of a spherical polymer-coated colloidal particle in a steady electric field is studied via "exact" numerical solutions of the electrokinetic equations. The hydrodynamic influence of the polymer is represented by a distribution of Stokes resistance centers. With neutral polymer, charge resides on the underlying bare particle, whereas for polyelectrolytes, the charge is distributed throughout the coating. The coatings may be brush-like or have long tails. As expected, neutral coatings lower the mobility because of increased drag and a decrease in the effective charge behind the shear surface. For polyelectrolyte coatings, the behavior is more complex. For example, the mobility becomes independent of the ionic strength and particle size when Donnan equilibrium prevails inside the coating and the coating is thick relative to the Brinkman screening length (square root of the coating permeability). In this limit, the mobility follows from a simple balance of forces within the coating and, therefore, becomes proportional to the fixed charge density and the coating permeability. If the permeability is sufficiently high, the mobility of a polyelectrolyte-coated particle may exceed that of its bare counterpart with the same net charge. In general, the effects of polarization and relaxation are as important for coated particles as they are for bare particles. (C) 2003 Elsevier Science (USA). All rights reserved.