Measurement of regional cerebral blood flow in vivo has proved useful in the study of normal and diseased states in the brain. This circumstance has led to a variety of techniques for its quantitative determination and has continued to motivate the search for ever safer and more accurate methods of measurement. Recently, the use of nuclear magnetic resonance (NMR) in medical imaging has stimulated efforts to make it the basis for a non-invasive method of measuring flow in the brain. New advances in fast NMR imaging (MRI) provide data potentially amenable to analysis by tracer-kinetic methods. Such an analysis has not previously been available. In this paper we present theoretical results that may permit measurement of brain blood flow by NMR. The data interpreted by our model are those generated by a novel MRI protocol developed by Perman et al. (1992, Magn. Reson. Med. 28, 74-83; Radiology 185(P), Abstr. 154, 127) that is entirely compatible with existing routine MRI procedures. These data are fast dynamic NMR signals that reflect passage of an intravenously administered paramagnetic contrast agent serving as a plasma tracer. Our equations show how to use such data sequences to determine plasma mean transit time, plasma volume, and plasma and whole-blood flow in arbitrarily selected regions of interest in the brain. The theory accounts rigorously for recirculation of tracer to the imaged regions. Our analysis provides an explanation for the linear relationship observed experimentally by others between regional vascular volumes and time integrals of vascular-tracer residue curves, and shows that this relationship remains valid in the presence of tracer recirculation.