A detailed and quantitative analysis of secondary active transport mechanisms in membrane vesicles is complicated by heterogeneity of the vesicles. Functional heterogeneity can be demonstrated by the time-dependence of isotope exchange of any solute at equilibrium. The need for more than one rate constant in the fit proves functional heterogeneity. To treat the heterogeneity quantitatively, it is suggested to subject entire time curves of exchange to inverse Laplace transformations that yield the corresponding distribution of rate constants. The computer program CONTIN by Provencher (1982a, b, c) can be used to carry out such a transformation. The distribution of rate constants under a particular set of conditions can be used to calculate a highly reliable initial rate. In addition, for spherical vesicles a mean, surface area-averaged permeability constant can be calculated if the size distribution of the vesicle population is known by other measurements and this size distribution is independent of the permeability distribution. Kinetic measurements under equilibrium conditions on the rabbit intestinal Na-glucose transporter indicate (using Cleland's nomenclature) an ordered iso-bi-bi mechanism with glide symmetry for substrate and co-substrate binding to the transporter at one interface and release at the other (first-in-first-out) (Hopfer & Groseclose, 1980). The kinetics are consistent with a gated pore mechanism of coupled Na-glucose cotransport. A similar mechanism seems to hold for renal Na-lactate cotransport (Mengual et al., 1983).