Recent crystallographic studies suggested that fully liganded human hemoglobin can adopt multiple quaternary conformations that include the two previously solved relaxed conformations, R and R2, whereas fully unliganded deoxyhemoglobin may adopt only one T (tense) quaternary conformation. An important unanswered question is whether R, R2, and other relaxed quaternary conformations represent different physiological states with different oxygen affinities. Here, we answer this question by showing the oxygen equilibrium curves of single crystals of human hemoglobin in the R and R2 state. In this study, we have used a naturally occurring mutant hemoglobin C (β6 Glu→Lys) to stabilize the R and R2 crystals. Additionally, we have refined the x-ray crystal structure of carbonmonoxyhemoglobin C, in the R and R2 state, to 1.4 and 1.8 Å resolution, respectively, to compare precisely the structures of both types of relaxed states. Despite the large quaternary structural difference between the R and R2 state, both crystals exhibit similar noncooperative oxygen equilibrium curves with a very high affinity for oxygen, comparable with the fourth oxygen equilibrium constant (K(4)) of human hemoglobin in solution. One small difference is that the R2 crystals have an oxygen affinity that is 2-3 times higher than that of the R crystals. These results demonstrate that the functional difference between the two typical relaxed quaternary conformations is small and physiologically less important, indicating that these relaxed conformations simply reflect a structural polymorphism of a high affinity relaxed state.