The purpose of this investigation was to explore the mechanistic bases of the hyperbolic relationship between power and the tolerable duration of severe-intensity exercise by assessing the kinetics of intramuscular phosphocreatine concentration ([PCr]) and pH during prediction trials performed both in normoxia and hyperoxia. It was hypothesised that the inspiration of hyperoxic gas would increase the asymptote of the power-duration relationship, i.e. the critical power (CP), without altering the curvature constant (W′). It was also hypothesised that the tolerable duration of exercise, irrespective of the work-rate within the severe-intensity domain, would be associated with the attainment of the same, critically low [PCr] and pH values as determined using ³¹P magnetic resonance spectroscopy (³¹P-MRS). Following ethical approval, seven male subjects (mean ± SD, age 30 ± 9 years) completed four constant work-rate, knee-extension exercise bouts to exhaustion (Tlim range: 3-10 min) both in normoxia (N) and hyperoxia (H; 70% O₂) inside the bore of 1.5 T superconducting magnet. The inspirates and work-rates were administered in a single-blind, randomised order. Individual power-time relationships were established using the hyperbolic model [time = W′/(power-CP)] and the overall rate of decline in [PCr] was calculated as the mean response time (MRT). Paired samples t-tests were used to assess differences between conditions in CP and W′. End-exercise [PCr] and pH were compared across inspirates and work-rates using two-way repeated measures ANOVAs. Significance was accepted at P<0.05. The CP was significantly higher in hyperoxia (N:16.1 ± 2.6 vs. H:18.0 ± 2.3 W; P<0.05), while the W′ parameter was not significantly altered (N:1.92 ± 0.70 vs. H:1.48 ± 0.31 kJ; P>0.05). The [PCr] at the limit of tolerance (~8% of resting baseline) during each of the four trials was not significantly different either in normoxia or hyperoxia (F6,18 = 1.43, P>0.05). The end-exercise pH (~6.65) was likewise unaffected by work-rate and the inspired oxygen fraction (F6,18 = 1.35, P>0.05). The overall rate at which [PCr] fell was attenuated in hyperoxia (MRT 116 ± 46 s) compared to normoxia (59 ± 20 s) (P<0.05). This study is the first to demonstrate that hyperoxia resulted in a significant increase in CP without altering the W′, and that hyperoxia extended the time to exhaustion during severe-intensity exercise by delaying the point at which [PCr] and pH reached values which might be considered to be limiting for continued muscle function. The present findings support the notion that the CP represents the highest sustainable oxidative metabolic rate and indicate that the W′ (and thus the nature of fatigue >CP) is related to muscle PCr availability and/or the attainment of a low muscle pH.