The recently established single-shot technique of echo-planar imaging of intravoxel incoherent motion (IVIM) for determining and imaging the variations of microscopic motions of water has been applied to studies of water perfusion in phantoms and to in vivo studies of diffusion and perfusion in cat and human brains. The phantom results demonstrate that perfusion levels comparable with those found in vivo have easily observable and reproducible effects on signal amplitude that are consistent with previous IVIM theory. Reliable measurements of the diffusion coefficient in various types of brain tissue have been obtained. The results for white matter are consistent with the existence of anisotropic diffusion in oriented bundles of myelinated nerve fibers. The results for gray matter can be fitted to the IVIM theory and suggest a value of up to 14% for the fraction of the signal contributed by randomly perfusing fluid in normal cerebral cortex.