We compute the electroosmotic how in nonuniformly charged planar and cylindrical capillaries for the limit of low-Reynolds-number flows and thin Debye layers. Analytical formulae for the velocity field are provided for the general case of an arbitrary surface inhomogeneity but we also focus on various specific defect geometries. Many important features can be obtained from the simple lubrication approximation. The pressure jump induced by the presence of such surface defects is calculated and the possible occurrence of recirculating flows is discussed, as are effects of the flow perturbations on dispersion in capillary electrophoresis.