This research aimed to identify relations of cognitive and power capacities with reactive agility in pubescent boys (n = 55) and girls (n = 46). Cognitive abilities were evaluated by the Stroop test, while the BlazePod system was used to evaluate agility performance conducting 20 yard shuttle and triangle tests of non-reactive (TCODS) and reactive agility (TRAG), respectively. Performance in jumping power was assessed through the squat jump (SJ), countermovement jump (CMJ), and drop jump (DHJ) utilising the Opto Jump system (Microgate, Bolzano, Italy), while sprinting ability over distances of 10 and 20 m was measured using a photocells system. A principal component was extracted from the four Stroop test variables using factor analysis. Forward stepwise multiple regression analysis was conducted separately for boys and girls to evaluate the multivariate relationships among the predictors and the criterion. Among boys, 80% of the TRAG variance was explained (MultipleR = 0.9), with TCODS and SJ as significant predictors (β = 0.53 and −1.01, respectively). For girls, the TCODS was the significant predictor (β = 0.65), explaining 43% of the variance (MultipleR = 0.65). These results show that (i) cognitive abilities measured with the Stroop test were not a reliable tool for predicting TRAG, (ii) jumping power was a significant predictor of TRAG in boys, and (iii) TCODS was a significant predictor of TRAG in girls. The findings indicated that cognitive abilities do not significantly influence reactive agility in pubescent children. It seems that power features have a greater influence on reactive agility, particularly in boys who have more developed motor skills at this age compared to girls.