The power–duration relationship describes tolerance to high–intensity exercise. The hyperbola is defined by an asymptote (critical power; CP), and the rectangular curvature constant (W′). Exercise above CP results in predictable intolerance following progressive accumulation of locomotor muscle fatigue. CP and W′ are reduced in hypoxia however it is unclear how hypoxia affects the dynamics of locomotor muscle fatigue. OBJECTIVE To measure locomotor muscle fatigue dynamics and exercise tolerance during supra–CP constant exercise in hypoxia. METHODS Fourteen volunteers (24 ± 4 yr, 169 ± 11 cm, 70 ± 15 kg, 5 women, 9 men) completed four constant power tasks above CP to intolerance in normoxia (FIO2 = 0.21) and hypoxia (FIO2 = 0.14). We measured maximal locomotor power throughout constant power tasks with 5 s interleaved maximal isokinetic sprints. RESULTS There was no difference in CP and W′ in normoxia vs hypoxia (CP: t = 1.8, p = 0.106, CI∆ -42, 5; W′: Sum of ranks -39, 39, p = 0.999). No difference in V̇ O2peak in normoxia vs hypoxia (Interaction: F[3, 72] = 0.303, p = 0.824, η2 = 0.003; Condition: F[1, 24] = 0.440, p = 0.514, η2 = 0.01). No difference in locomotor fatigue dynamics in normoxia vs hypoxia (Interaction: F[7, 138] = 0.576, p = 0.775; Condition: F[1, 21] = 2.176, p = 0.155). Exercise tolerance was shortened in hypoxia during the longest constant power bout (t = 3.52, p = 0.005, CI∆ -328, -76 s). A power reserve was present at intolerance during the longest constant power bout and was smaller in hypoxia (t = 3.0, p = 0.011, CI∆ -164, -26 W). CONCLUSIONS Moderate hypoxia (FIO2 = 0.14) was insufficient to modify the intramuscular fatigue processes that underlie reductions in voluntary maximal isokinetic power in the supra–CP domain. Further, the power–duration relationship was not affected. This reinforces the relatively rigid confines and reproducibility of exercise tolerance above CP despite a powerful modifier in reproducing inspired PO2 similar to that found at ~10,000 ft.