The critical power (CP) model is based on the robust, hyperbolic relation between power output and the tolerable duration of high-intensity exercise; the asymptote is termed CP and the curvature constant W’ [1]. The model states that, when the required power exceeds the maximum power of the aerobic system (CP), task failure will concur with the depletion of the energy stores (W’). The consequence is that subjects will not be able to continue exercising after task failure, unless the power output is decreased to below CP [2]. The purpose of the present study was to test these hypotheses. Eight healthy men each performed an incremental test on a cycle ergometer to determine the power at their VO2max (P100%), followed by a familiarisation and 4 time-to-task failure tests (TFT) at P120%. The first 3 TFTs were used to determine the best time-to-task failure at P120%. The last TFT was a similar test, but now the subjects were instructed to continue exercising until they had reached their best time and then continue as long as possible at a reduced power of P105%. Blood lactate concentration [BLa] was measured at task failure and after 5 min of recovery at 60W. Oxygen uptake (VO2) was measured to determine VO2max and calculate the anaerobic energy production based on the accumulated oxygen deficit (AOD) method [3]. Values are means ± SD, compared with paired t-tests. All subjects were able to reach their best time at P120% during the final TFT (182 ± 32 s). 6 subjects were able to continue exercising at P105% for over 25 s (mean time was an extra 56 ± 47 s). [BLa] was not different between P120% and P105% at task failure (13.5 ± 2.8 vs. 15.7 ± 1.9 mM), but was different after the 5-min recovery (14.3 ± 1.7 vs. 15.7 ± 1.9 mM, p<0.01). Heart rate was higher after P105% than after P120% (185 ± 9 vs. 179 ± 8 bpm, p<0.01). There was no difference between VO2 after P120% and P105% (49.0 ± 5.6 vs. 51.3 ± 4.0 ml/kg/min). The calculated anaerobic energy production at P105% resulted in negative values for 7 of the subjects. The observation that 7 out of 8 subjects were able to continue exercising at P105% shows that, supported by the observed increase in [BLa], they were able to produce an additional amount of anaerobic energy after reaching task failure at P120%. This implies that task failure at P120% was not caused by the depletion of a fixed of anaerobic work, as proposed by the CP model. Furthermore, the paradoxical negative anaerobic energy contribution at P105%, as predicted by the AOD method, can only be explained by a reduction in efficiency at higher intensities. As a consequence, the CP model will underestimate the anaerobic energy. These results indicate not only that the W’ cannot be used as accurate estimation of total anaerobic work, but also that task-failure during high-intensity exercise is not directly caused by depletion of anaerobic energy stores.