Bedding-parallel permeability of illite-rich shale of the Wilcox formation has been investigated using distilled water and 1 M solutions of NaCl, KCl, and CaCl2 as pore fluids. Despite low modal concentrations of swelling clays, specimens expand upon fluid saturation and permeabilities depend on fluid composition. Permeabilities to flow of 1 M CaCl2 are 3--5 times greater than values measured for the other pore fluids, suggesting sensitivity to exchange of divalent cations for monovalent cations at clay mineral surfaces. Permeabilities of individual samples exhibit nonrecoverable changes with sequential changes in composition of incoming fluid. Permeabilities k at varying effective pressure Pe fit a cubic law k = k0 <1 - (Pe/P1)m>3, where m and P1 are independent of fluid composition, and k0 is greater for transport of 1 M CaCl2 than that for transport of the other pore fluids. Assuming that fluid conduits have crack-like dimensions, the lack of sensitivity of m and P1 to fluid composition suggests that surface roughness and asperity stiffness of conduits are unaffected by cation exchange, while changes in k0 reflect changes in the clay-fluid interfaces of the connected pore space.