A method is presented to identify and quantify hypoxia in human head-and-neck tumours based on dynamic [18F]-Fmiso PET patient data, using a model for the tracer transport. A compartmental model was developed, inspired by recent immunohistochemical investigations with the tracer pimonidazole. In order to take the trapping of the tracer and the diffusion in interstitial space into account, the kinetic model consists of two compartments and a specific input function. This voxel-based data analysis allows us to decompose the time-activity curves (TACs) into their perfusion, diffusion and hypoxia-induced retention components. This characterization ranges from well perfused tumours over diffusion limited hypoxia to strong hypoxia and necrosis. The overall shape of the TAC and the model parameters may point at the structural architecture of the tissue sample. The model addresses the two main problems associated with hypoxia imaging with PET. Firstly, the hypoxic areas are spatially separated from well perfused vessels, causing long diffusion times of the tracer. Secondly, tracer uptake occurs only in viable hypoxic cells, which constitute only a small subpopulation in the presence of necrosis. The resulting parameters such as the concentration of hypoxic cells and the perfusion are displayed in parameter plots ('hypoxia map'). Quantification of hypoxia performed with the presented kinetic model is more reliable than a criterion based on static standardized uptake values (SUV) at an early timepoint, because severely hypoxic/necrotic tissues show low uptake and are thus overlooked by SUV threshold identification. The derived independent measures for perfusion and hypoxia may provide a basis for individually adapted treatment planning.