PURPOSE: The main aim of the study was to investigate whether anaerobic capacity, estimated as the accumulated oxygen deficit (AOD) and the curvature constant of the power-duration relationship (W’), remain constant during supramaximal exercise to exhaustion at constant-load and all-out exercise. The secondary aim was to determine the relationship between AOD and W’ during supramaximal exercise to exhaustion at constant-load and all-out exercise. METHODS: In a cross-over design, 21 male cyclists (means ± standard deviations for age, height, mass and maximal oxygen uptake (V†O2max) of 40 ± 6 years, 1.81 ± 0.08 m, 80 ± 8 kg and 58 ± 7 ml•kg-1•min-1, respectively) completed a ramp test to determine the gas exchange threshold, followed, on a separate day, by step and ramp tests to determine the V†O2-power output relationship and maximal oxygen uptake, respectively. Subsequently and on separate days, AOD and W’ were determined for a cycle to exhaustion at a constant-load corresponding to 112.5% V†O2max and a 3-min all-out (3AO) test. AOD was determined as the difference between accumulated oxygen demand, predicted from linear projection of the V†O2-power output relationship, and accumulated oxygen uptake. W’ was considered as work completed above critical power (CP). CP was determined as the average power output in the last 30 s of the 3AO test. RESULTS: There were no differences between the constant-load and 3AO tests for duration (164 ± 46 s vs. 180 ± 0 s, respectively; P = 0.170), work completed (60.8 ± 17.3 kJ vs. 67.7 ± 9.84 kJ, respectively; P = 0.057) or average power output (376 ± 55 W vs. 376 ± 55 W, respectively; P = 0.882). However, there were differences between the constant-load and 3AO test for AOD (P = 0.004) and W’ (P = 0.010). The highest AOD was in constant-load (4.18 ± 0.95 L vs. 3.68 ± 0.98 L), whilst W’ was greatest in 3AO (9.55 ± 4.00 kJ vs. 11.37 ± 3.84 kJ). AOD and W’ were correlated during the constant-load (P < 0.001, r = 0.654) and 3AO (P < 0.001, r = 0.664) tests. CONCLUSIONS: Despite AOD and W’ being correlated during constant-load and 3AO tests, they were different in the constant-load compared to 3AO test. Moreover, the fact that AOD was greatest in constant-load test whilst W’ was greatest in 3AO suggests that the mechanisms underpinning AOD and W’ may be different, and affected by factors other than anaerobic capacity.