To date no satisfactory method has been available for the quantitative in vivo measurement of the complex hepatic blood flow. In this study two modelling approaches are proposed for the analysis of liver blood flow using positron emission tomography (PET). Five experiments were performed on three foxhounds. The anaesthetised dogs were each given an intravenous bolus injection of oxygen-15 labelled water, and their livers were then scanned using PET. Radioactivity in the blood from the aorta and portal vein was measured directly and simultaneously using closed external circuits. Time-activity curves were constructed from sequential PET data. Data analysis was performed by assuming that water behaves as a freely diffusible tracer and adapting the standard one-compartment blood flow model to describe the dual blood supply of the liver. Two particular modelling approaches were investigated: the dual-input model used both directly measured input functions (i.e. using the hepatic artery and the portal vein input, determined from the radioactivity detected in the aorta and portal vein respectively) whereas the single-input model used only the measured arterial curve and predicted the corresponding portal input function. Hepatic arterial flow, portal flow and blood volume were fitted from the PET data in several regions of the liver. The resulting estimates were then compared with reference blood flow measurements, obtained using a standard microsphere technique. The microspheres were injected in a separate experiment on the same dogs immediately prior to PET scanning. Whilst neither the single- nor the dual-input models accurately reproduced the arterial reference flow values, the flow values from the single-input model were closer to the microsphere flow values. The proposed single-input model would be a good approximation for liver blood flow measurements in man. The observed discrepancies between the PET and microsphere flow values may be due to the inherent temporal and spatial heterogeneity of liver blood flow. The results presented suggest that adaptation of the standard one-compartment blood flow model to describe the dual blood supply of the liver is limited and other flow tracers have to be considered for quantitative PET measurements in the liver.