[F-18]fluoromisonidazole (FMISO), a positron-emitting nitroimidazole, binds preferentially to hypoxic cells. It has been used to image hypoxia in human tumors with positron emission tomography (PET). In order to quantify tumor oxygenation status from these PET data, a kinetic model of FMISO cellular bioreduction has been developed to relate cellular oxygen concentration to the cellular FMISO reaction rate constant, kappa A. Also, a compartmental model of FMISO transport and metabolism has been developed to compute the volume average kappa A in tissue regions from [F-18]FMISO PET time-activity data. This compartmental model was characterized using Monte Carlo simulations and [F-18]FMISO PET time-activity data. The model performed well in Monte Carlo simulations; performance was enhanced by fixing three of the seven model parameters at physiologically reasonable values. The four parameters optimized were blood flow rate, kappa A for two partial volume/spillover correction factors. The model was able to accurately determine kappa A for a variety of computer-generated time-activity curv including those for hypothetical heterogeneous tissue regions and poorly perfused tissue regions. The model was also able to fit [H-3]FMISO time-activity data from 36B-10 rat tumors as well as [F-18]FMISO PET time-activity data from a human patient with a base of the tongue squamous cell carcinoma. The kappa A values in muscles ROIs were comparable to those in well-oxygenated cell monolayers while kappa A values in tumor ROIs were greater, suggesting the presence of hypoxic cells in the tumor.