K-Cl cotransport in LK sheep erythrocytes is activated by osmotic swelling and inhibited by shrinkage. The mechanism by which changes in cell volume are transduced into changes in transport was investigated by measuring time courses of changes in transport after osmotic challenges in cells with normal and reduced Mg concentrations. When cells of normal volume and normal Mg are swollen, there is a delay of 10 min or more before the final steady-state flux is achieved, as there is for swelling activation of K-Cl cotransport in erythrocytes of other species. The delay was shown to be independent of the extent of swelling. There was also a delay after shrinkage inactivation of cotransport. Reducing cellular Mg concentration activates cotransport. Swelling of low-Mg cells activates cotransport further, but with no measurable delay. In contrast, there is a delay in shrinkage inactivation of cotransport in low-Mg cells. The results are interpreted in terms of a three-state model: [formula see text] in which A state, B state, and C state transporters have relatively slow, intermediate, and fast transport rates, respectively. Most transporters in shrunken cells with normal Mg are in the A state. Swelling converts transporters to the B state in the rate-limiting process, followed by rapid conversion to the C state. Reducing cell Mg also promotes the A-->B conversion. Swelling of low-Mg cells activates transport rapidly because of the initial predominance of B state transporters. The results support the following conclusions about the rate constants of the three-state model: k21 is the rate constant for a Mg-promoted process that is inhibited by swelling; k12 is not volume sensitive. Both k23 and k32 are increased by swelling and reduced by shrinkage; they are rate constants for a single process, whereas k12 and k21 are rate constants for separate processes. Finally, the A-->B conversion entails an increase in Jmax of the transporters, and the B-->C conversion entails an increase in the affinity of the transporters for K.