The tolerable duration (t_lim) of very-heavy intensity (VH) exercise demonstrates a hyperbolic relationship with the external power output (P); the curvature constant (W’) being equivalent to a fixed amount of work above the power asymptote (critical power; CP) which is the upper limit for steady state exercise [1]. The physiological determinants of CP and W’ are unclear, however. As the ability to sustain exercise (i.e. prolong t_lim) is associated with the capacity to transport and utilise O₂, we were interested in the relationship between pulmonary O₂ uptake (VO₂) kinetics and the P-t_lim parameters. We hypothesised that: 1) a high CP would be associated with a fast fundamental VO₂ time constant (τ), by minimising the O₂ deficit accumulation at a given P; and 2) W′ (suggested to reflect the rate of muscular fatigue-induction [2]) would relate to the slow component magnitude (ΔVO₂sc), via hastening the attainment of the upper limit of VO₂ (VO₂max). Fourteen healthy men, aged 20−34 yr gave informed consent to undertake cycle ergometry (Excalibur Sport, Lode, NL) with breath-by-breath VO₂ measurement by mass-spectrometry and turbinometry (MSX, Morgan Medical, UK). On different days they performed: 1) an incremental-ramp to estimate lactate threshold (LT); 2) a series of constant-work rate (CWR) tests to t_lim to determine VO₂max, CP and W′; and 3) repeated CWR tests, normalised to induce t_lim in 6 min (WR₆), for estimation of τ_VH and ΔVO₂sc. Seven men also repeated CWR at 80% LT (MOD) for estimation of τ_MOD. LT averaged 2.11±0.37 l/min (26±5 ml/kg/min) and VO₂max 4.18±0.49 l/min (51±7 ml/kg/min). WR₆ (296±29 W) was tolerated for 365±17 s. CP ranged 171 to 294 W and τ_VH 18.3 to 37.6 s in these relatively “fit” young subjects. In addition, τ_MOD and τ_VH did not differ (t-test p>0.05; mean difference -0.1±1.8 s; range -1.4 to +2.5 s; c.f. [3]), each strongly and inversely correlated to CP: R²=0.91 and 0.90, respectively. W′ (range 12.8−29.9 kJ) was directly correlated (R²=0.71) with ΔVO₂sc (425−957 ml/min). Our findings support the notion that rapid VO₂ kinetics reduce the stress to homeostasis, allowing high power outputs to be sustained. Although the design of this study did not allow resolution of the mechanisms determining the correlation between CP and τ_VH (and τ_MOD), the projected relationship is consistent with reported values of CP and τVO₂ in subjects ranging from elite endurance athletes to the healthy elderly [4,5]. The VO₂sc likely reflects supplementary muscle O₂ consumption due to additional fibre recruitment; this presaging muscular fatigue. W’, a notional energy store [1], may therefore better reflect the accumulation of fatigue-related metabolites to a ‘critical’ level [2]: a notion supported by the correlation of ΔVO₂sc and W’. Collectively, these data support VO₂ kinetics as a major determinant of very-heavy intensity exercise tolerance.