Two complementary continuum theories of electrokinetic transport are examined with particular emphasis on the equivalent conductance of binary electrolytes. The "small ion" model [R.M. Fuoss, L Onsager, J. Phys. Chem. 61 (1957) 668] and "large ion" model [R.W. O'Brien, L.R. White, J. Chem. Soc. Faraday Trans. 2 (74) (1978) 1607] are both discussed and the "large ion" model is generalized to include an ion exclusion distance and to account in a simple but approximate way for the Brownian motion of all ions present. In addition, the "large ion" model is modified to treat "slip" hydrodynamic boundary conditions in addition to the standard "stick" boundary condition. Both models are applied to the equivalent conductance of dilute KCl, MgC2, and LaCl3 solutions and both are able to reproduce experimental conductances to within an accuracy of several tenths of a percent. Despite fundamental differences in the "small ion" and "large ion" theories, they both work equally well in this application. In addition, both "stick-large ion" and "slip-large ion" models are equally capable of accounting for the equivalent conductances of the three electrolyte solutions. (C) 2010 Published by Elsevier Inc.