Transcellular oxygen flux was modelled mathematically in the aerobic skeletal muscles of perciform fish species living at widely different temperatures (Antarctica, sub-Antarctica and the Mediterranean Sea). Using structural data derived from stereological analysis of electron micrographs, mean fibre P(O(2)) was calculated on the basis of temperature-corrected rates of mitochondrial respiration and oxygen diffusion. The mean muscle fibre diameter (MFD) among Antarctic notothenioids was in the range 17-61 microm and mitochondrial volume density, Vv(mit,f), was 0.27-0.53, but capillary-to-fibre ratio varied only between 1.2 and 1.5. For a mean capillary P(O(2)) of 6 kPa, the model predicted a mean tissue P(O(2)) in the range 0.7-5.8 kPa at the estimated maximum aerobic capacity (M(O(2)max)). The lowest levels of tissue oxygenation were found in the pectoral muscle fibres of the icefish Chaenocephalus aceratus, which lacks the respiratory pigments haemoglobin and myoglobin. Red-blooded notothenioids found in the sub-Antarctic had a similar muscle fine structure to those caught south of the Antarctic Convergence, with an MFD of 20-41 microm and Vv(mit,f) of 0.27-0.33, resulting in an estimated mean P(O(2)) of 4-5 kPa at M(O(2)max). Mean tissue P(O(2)) in the sub-Antarctic icefish Champsocephalus esox, with greater MFD and Vv(mit,f), 56 microm and 0.51, respectively, was calculated to exceed 1 kPa at winter temperatures (4 degrees C), although oxidative metabolism was predicted to be impaired at the summer maximum of 10 degrees C. At the high end of the thermal range, related perciform species from the Mediterranean had a negligible drop in intracellular P(O(2)) across their small-diameter fibres, to a minimum of 5.4 kPa, comparable with that predicted for Trematomus newnesi from the Antarctic (5.6 kPa) with a similar MFD. These data suggest that, within a single phylogenetic group, integrative structural adaptations potentially enable a similar degree of tissue oxygenation over a 20 degrees C range of environmental temperature in the red-blooded notothenioids, and that this is compromised by the lack of respiratory pigments in the icefishes. The mean capillary radius was 1.5 times greater in the two icefish than in the other notothenioids, and the model simulations indicate that the evolution of wide-bore capillaries is essential to maintain tissue oxygenation in the absence of respiratory pigments.