As groundwater passes through porous rocks, exchange of oxygen between the fluid and the solid matrix causes a change in the oxygen isotope concentrations in both water and rock. If the rate at which the exchange takes place can be estimated (as a function of the isotope concentrations and temperature), then the time taken form a rock/water system to come to equilibrium with respect to isotope concentration might be calculated. In this paper, conservation laws are used to derive equations for the isotope transport in a porous medium; these are combined with fluid flow equations and a simple equation describing the rate of oxygen isotope exchange between the water and the rock. The resulting set of equations is solved analytically for the zero-dimensional (lumped-parameter) model, and numerically, using typical parameters, for the one-dimensional case. ¿ American Geophysical Union 1989