Deuterium NMR is employed in concert with multicompartment kinetic analysis for measurement of tissue blood flow and perfusion through a bolus administration of D2O as a freely diffusible tracer. The traditional single-compartment and two-compartment in-parallel flow models with no tracer recirculation are briefly discussed. The two-compartment in-series flow model with recirculation is developed to account for reflow of the stable (slowly excreted) deuterium tracer. With this model a monoexponential tracer washout curve is predicted. The rate of blood flow and tissue perfusion is readily extracted by three-parameter monoexponential analysis of the residue decay curve. A three-compartment model with recirculation, incorporating one compartment in-series with two compartments in-parallel, is developed for analysis of biexponential tracer washout curves. With this model the flow rates through the two in-parallel compartments (i.e., fast and slow) and the volume fractions of these two compartments are obtained by five-parameter biexponential analysis of the residue decay curve. Application of these multicompartment tracer-recirculation flow models is demonstrated with in situ determinations of murine RIF-1 tumor blood flow and tissue perfusion. The blood flow rates determined by deuterium NMR and analyzed by the multicompartment flow models agree well with those determined by others using radiolabels. A companion article (S.-G. Kim and J.J.H. Ackerman, Cancer Res. 48, 3449-3453, 1988) discusses in more depth the practical aspects of applying these multicompartment models to tumor blood flow measurement.