A limitation of magnetization transfer techniques for studying enzyme kinetics in vivo has been the difficulty of treating systems with more than two exchanging species. This problem was addressed in the original papers describing saturation transfer. Since then, a number of approaches have been devised to study these complex situations. Here, we present a method based on the transient saturation transfer experiment in which spin-lattice relaxation time constants and reaction rates are obtained from the same magnetization transfer data. This technique is particularly suitable for biological samples. We apply the method to evaluate flux balance in the three-site linear exchange network composed of ATP, creatine phosphate, and inorganic phosphate in the isolated, perfused rat heart and show that the method yields reasonable values for the reaction velocities of ATP synthesis and degradation.