Abstract The transmural potential difference (PD) measured in vitro with paired everted jejunal and ileal sacs of rat small intestine is strongly influenced by the concentration of Na + and by the presence and concentration of actively transported sugars. Changes in PD, ΔPD, following the addition of certain sugars have been assumed to reflect changes in the rate of Na + entry. Double reciprocal plots, 1/ΔPD vs. 1/[sugar], are suggestive of saturation phenomena interpretable in terms of a ternary interaction of Na +, sugar and a mobile carrier in the brush border membrane. Reasoning along these lines, comparison of the kinetics observed with Tris +, a non-penetrating ion, and with K +, a penetrating ion, suggest that K + is a competitive inhibitor for Na + interaction with the sugar carrier. The dissociation constants for the various equilibria which may be assumed to occur in a system containing carrier, Na + or K + and sugar have been evaluated by extrapolation from plotted values and by computer iterative analysis. The effect of K + replacement of Na + with rat preparations differs somewhat from the effect with rabbit ileum reported by others although, in both, PD and short-circuit current measurements rise in response to increases in Na + and/or sugar concentrations. The need is thus indicated for consideration of two kinetic models: one in which there is a high degree of interaction between the ion-binding and sugar-binding sites of the carrier, a model which appears to be appropriate for the rat, and another in which interaction between these sites is minimal, a model which appears to fit the data for the rabbit.