Hemopure (Biopure; Cambridge, MA) and PolyHeme (Northfield Laboratories; Evanston, IL) are two acellular hemoglobin-based O2 carriers (HBOCs) currently in phase III clinical trials for use as red blood cell substitutes. The most common adverse side effect that these HBOCs exhibit is increased vasoconstriction. Autoregulatory theory has been presented as a possible explanation for this physiological effect, where it is hypothesized that low-affinity HBOCs over-deliver O2 to tissues surrounding arterioles, thereby eliciting vasoconstriction. In this paper, we wanted to investigate HBOC oxygenation of tissue surrounding a capillary, which is the smallest element of the circulatory system. An a priori model has been developed in which the performance of mixtures of acellular HBOCs (synthesized by our group and others) and human red blood cells (hRBCs) has been simulated using a Krogh tissue cylinder model (KTCM) comprising a capillary surrounded by a capillary membrane and skeletal muscle tissue in cylindrical coordinates with specified tissue O2 consumption rates and Michaelis-Menten kinetics. In this study, the total hemoglobin (hRBCs and HBOCs) concentration was kept constant. The HBOCs studied possessed O2 affinities that were higher and lower compared to hRBCs (P50's spanned 5-55 mmHg), and the equilibrium binding/release of oxygen to/from the HBOCs was modeled using the Adair equation. At normoxic inlet pO2's, there was no correlation between O2 flux out of the capillary and the O2 affinity of the HBOC. However, a correlation was found between the average pO2 tension in the capillary and the O2 affinity of the HBOC. Additionally, we studied the change in the O2 equilibrium curve of HBOCs with different O2 affinities over a wide range of inlet pO2's and found that changing the inlet pO2 greatly affected which HBOC, having a unique O2 affinity, best delivered O2 to the surrounding tissue. The analysis of oxygen transport presented could lead to a better prediction of which acellular HBOC is best suited for a specific transfusion application that many times depends on the capillary inlet pO2 tension.