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Tolerance to high-intensity constant-power (P) exercise is well described by a hyperbola with two parameters: a curvature constant (W′) and power asymptote termed “critical power” (CP). Since the ability to sustain exercise is closely related to the ability to meet the ATP demand in a steady state, we reasoned that pulmonary O₂ uptake (V̇o₂) kinetics would relate to the P-tolerable duration (t_lim) parameters. We hypothesized that 1) the fundamental time constant (τV̇o₂) would relate inversely to CP; and 2) the slow-component magnitude (ΔV̇o_2sc) would relate directly to W′. Fourteen healthy men performed cycle ergometry protocols to the limit of tolerance: 1) an incremental ramp test; 2) a series of constant-P tests to determine V̇o_2max, CP, and W′; and 3) repeated constant-P tests (WR₆) normalized to a 6 min t_lim for τV̇o₂ and ΔV̇o_2sc estimation. The WR₆ t_lim averaged 365 ± 16 s, and V̇o_2max (4.18 …