Key points The power‐asymptote (critical power; CP) of the hyperbolic power–time relationship for high‐intensity exercise defines a threshold between steady‐state and non‐steady‐state exercise intensities and the curvature constant (W′) indicates a fixed capacity for work >CP that is related to a loss of muscular efficiency. The present study reports novel evidence on the muscle metabolic underpinnings of CP and W′ during whole‐body exercise and their relationships to muscle fibre type. We show that the W′ is not correlated with muscle fibre type distribution and that it represents an elevated energy contribution from both oxidative and glycolytic/glycogenolytic metabolism. We show that there is a positive correlation between CP and highly oxidative type I muscle fibres and that muscle metabolic steady‐state is attainable CP. Our findings indicate a mechanistic link between the bioenergetic characteristics of muscle fibre types and the power–time relationship for high‐intensity exercise. Abstract We hypothesized that: (1) the critical power (CP) will represent a boundary separating steady‐state from non‐steady‐state muscle metabolic responses during whole‐body exercise and (2) that the CP and the curvature constant (W′) of the power–time relationship for high‐intensity exercise will be correlated with type I and type IIx muscle fibre distributions, respectively. Four men and four women performed a 3 min all‐out cycling test for the estimation of CP and constant work rate (CWR) tests slightly >CP until exhaustion (Tlim), slightly CP Tlim isotime to test the first hypothesis. Eleven men performed 3 min all‐out tests and donated muscle biopsies to test the second hypothesis. Below CP, muscle [PCr] [42.6 ± 7.1 vs. 49.4 ± 6.9 mmol (kg d.w.)−1], [La−] [34.8 ± 12.6 vs. 35.5 ± 13.2 mmol (kg d.w.)−1] and pH (7.11 ± 0.08 vs. 7.10 ± 0.11) remained stable between ∼12 and 24 min (P > 0.05 for all), whereas these variables changed with time >CP such that they were greater [[La−] 95.6 ± 14.1 mmol (kg d.w.)−1] and lower [[PCr] 24.2 ± 3.9 mmol (kg d.w.)−1; pH 6.84 ± 0.06] (P < 0.05) at Tlim (740 ± 186 s) than during the