1. The kinetics of phosphoglucomutases from different sources are discussed and it is concluded that on the available evidence there are in all cases three possible mechanisms for the reaction. These are an indirect transfer of phosphate involving the phosphoenzyme (mechanism 1), a direct transfer of phosphate (mechanism 2), and an intermolecular transfer of phosphate from glucose 1,6-diphosphate to the substrate (mechanism 3). Conventional net flux measurements are shown not to differentiate between these mechanisms. 2. Flux equations are developed and it is shown that there are three flux ratios that characterize and distinguish between the mechanisms. 3. To examine these flux ratios induced-transport tests are described with (14)C- and (32)P-labelled substrates. The fluxes determined with (14)C- and (32)P-labelled substrates are also compared at chemical equilibrium. 4. With rabbit muscle phosphoglucomutase the results of these tests were completely consistent with mechanism 1 and unequivocally excluded any substantial part of the reaction proceeding by mechanism 2 or mechanism 3. Evidence was also obtained for an isomerization of the phosphoenzyme with an apparent rate constant about 4.5x10(7)sec.(-1). Taking into account the activity coefficients of the substrates the true rate constant appears to be about one-sixth of this value. 5. Isotope effects and non-ideal behaviour of the solutions are discussed and the activity coefficients of the substrates are shown to be equal by measurement of the depression of freezing point. It is concluded that these factors do not influence the tests significantly. 6. Alternative mechanisms are considered and it is concluded that the tests show that the glucose residue is transferred directly, that the phosphate is transferred indirectly with one intermediate phosphate, and that there is an isomerization of the free phosphoenzyme without reference to any other details of the reaction. Further, no assumptions are required about the constancy of rate constants. 7. The relative merits of induced transport and product inhibition for detecting isomerization of the enzyme are discussed. It is concluded that the induced-transport test is more sensitive and that its interpretation is less equivocal. 8. The application of the tests to other enzyme systems is briefly considered.