Previous work demonstrated a highly reproducible cortical hierarchy of neural timescales at rest, with sensory areas displaying fast, and higher-order association areas displaying slower timescales. The question arises as to how such stable hierarchies give rise to adaptive behavior that requires flexible adjustment of temporal coding and integration demands. Potentially, this lack of variability in the hierarchical organization of neural timescales could reflect the structure of the laboratory contexts. We posit that unconstrained paradigms are ideal to test whether the dynamics of neural timescales reflect behavioral demands. Here we measured timescales of local field potential activity while male rhesus macaques foraged in an open space. We found a hierarchy of neural timescales that differs from previous work. Importantly, although the magnitude of neural timescales expanded with task engagement, the brain areas’ relative position in the hierarchy was stable. Next, we demonstrated that the change in neural timescales is dynamic and contains functionally relevant information, differentiating between similar events in terms of motor demands and associated rewards. Finally, we demonstrated that brain areas are differentially affected by these behavioral demands. These results demonstrate that while the space of neural timescales is anatomically constrained, the observed hierarchical organization and magnitude are dependent on behavioral demands.