When measuring perfusion by arterial spin labeling, saturation of tissue macromolecular spins during arterial spin labeling greatly decreases tissue water magnetization, reducing the sensitivity of the technique. In this work, a theory has been developed for perfusion measurement by arterial spin labeling without saturation of macromolecular spins. A two-coil system was used to achieve arterial spin labeling without saturation of brain tissue macromolecular spins for NMR measurement of rat cerebral perfusion. The effects of cross-relaxation on the measurement of perfusion have been studied in the absence of macromolecular spin saturation, and it is demonstrated that at 4.7 Tesla, perfusion is underestimated by approximately 17% when the effect of cross-relaxation is neglected in the calculation of perfusion. However, assuming water to be a freely diffusable tracer, the effect of cross-relaxation is predicted to be flow independent, and it can, thus, be accounted for in the calculation of perfusion. The theory and experiments are presented to estimate tissue perfusion, magnetization transfer rate constants, and spin-lattice relaxation times of water and macromolecular spins in rat brain.