A competition assay of ⁸⁶Rb⁺ uptake in HeLa cells transfected with ouabain-resistant Na⁺-K⁺-ATPase mutants revealed a stimulation of ⁸⁶Rb⁺ uptake at low external concentrations (1 mM) of competitor (K⁺). Of the models that were tested, those that require that two K⁺ be bound before transport occurs gave the worst fits. Random and ordered binding schemes described the data equally well. General models in which both binding and transport were allowed to be cooperative yielded parameter errors larger than the parameters themselves and could not be utilized. Models that assumed noncooperative transport always showed positive cooperativity in binding. E327Q and E327L mutated forms of rat ₂ had lower apparent affinities for the first K⁺ bound than did wild-type rat ₂ modified to be ouabain resistant. The mutations did not affect the apparent affinity of the second K⁺ bound. Models that assumed noncooperativity in binding always showed positively cooperative transport, i.e., enzymes with two K⁺ bound had a higher flux than those with one K⁺ bound. Increases in external Na⁺ decreased the apparent affinity for K⁺ for all models and decreased the ratio of the apparent influx rate constants for E327L.