The aim of this study was to investigate possible associations between the curvature constant (W’) from the critical power model by two linear models with maximal accumulated oxygen deficit (MAOD) and performance in soccer players. Nine professional soccer players (age, 16.1±1.2 yrs) were recruited. The subjects performed an incremental maximal test, four bouts of 10 min of submaximal exercises, and three supra-maximal exercises to determine the MAOD, W’ and performance in soccer, which was assumed as time until exhaustion at each applied supra-maximal intensity. MAOD corresponded to 3.43±1.35 L and 52.18±19.86 ml•kg-1, while W’ determined by the linear distance time model (W’dt) was 193.7±52.2m, and W’ determined by the velocity over inverse of time model (W’tlim-1) was 185.9±60.4 m. No significant correlation was found between the W’s and MAOD. The only significant correlations were between the W’s with time limit (r=0.80 for W’dt and r=0.70 for W’tlim-1; P≤0.05). We can therefore conclude that W’ determined in treadmill running using these linear models allows the prediction of exhaustive efforts of approximately 130s duration, but is not associated with MAOD.