It is widely recognized that the intracellular oxygen tension (pO2) plays an important role in cellular function and metabolism. In experimental and theoretical consideration involving the role of the pO2 the values that are used usually are those for the pO2 at the exterior of cells, because these values can be more readily measured. Such an approach is based on the assumption that the intracellular pO2 is very similar to the extracellular pO2 because oxygen freely diffuses across cell membranes and within cells, at a rate that is similar to that in the extracellular media. For the past several years we have been developing and applying electron paramagnetic resonance (EPR) techniques to test directly whether there are intracellular gradients of pO2 and if so, where they occur and what factors determine them. We previously reported significant gradients between the average pO2 in the intracellular and extracellular compartments in cell suspensions (Glockner 1989). More recently we developed techniques that enabled us to measure simultaneously the concentration of oxygen within a specific compartment, the phagosomes of activated macrophages, and the extracellular compartment and found gradients of up to 48 microM under some conditions (James 1995). The precise mechanism of the intracellular-extracellular oxygen gradient remains uncertain. The possibilities include that the diffusion of oxygen is not as free as assumed (e.g. that the cell membrane can act as a barrier) and the occurrence of active transport of O2 out of the cells. We report here on the use of a simple theoretical approach to evaluate the values of three key parameters which might account for the observed intracellular-extracellular oxygen measurements: (1) oxygen consumption; (2) the diffusion coefficient of oxygen in the cytosol; (3) the solubility of oxygen in the cytosol. We used two different models for the relationship between the oxygen consuming compartment (assumed to be primarily the mitochondria) and the intracellular compartment in which the measurements were made (especially phagosomes): uniform and non-uniform distribution of the mitochondria. Using these models and consensus values from the literature, we were unable to account for the experimentally observed differences in pO2 between the intracellular and extracellular compartments. Also we found that with the variation of any one parameter we could not plausibly account for the measurements made in the phagosomal and extracellular compartments. There are at least three logical possibilities to account for these results: 1) this methodology is erroneous and/or produces artifacts in the system resulting in invalid results; 2) the observation of a gradient in oxygen concentration between these two compartments arises from significant simultaneous variations of more than one of the critical parameters which are used conventionally to calculate potential gradients in pO2; 3) there is another factor not considered in the model which accounts for the observation (e.g. active transport; significantly higher than expected barriers to oxygen diffusion in the membrane).