Human cognition is characterized by flexibility, the ability to select not only which action but which cognitive process to engage to best achieve the current behavioral objective. The ability to tailor information processing in the brain to rules, goals, or context is typically referred to as executive control, and although there is consensus that prefrontal cortex is importantly involved, at present we have an incomplete understanding of how computational flexibility is implemented at the level of prefrontal neurons and networks. To better understand the neural mechanisms of computational flexibility, we simultaneously recorded the electrical activity of groups of single neurons within prefrontal and posterior parietal cortex of monkeys performing a task that required executive control of spatial cognitive processing. In this task, monkeys applied different spatial categorization rules to reassign the same set of visual stimuli to alternative categories on a trial-by-trial basis.Wefound that single neurons were activated to represent spatially defined categories in a manner that was rule dependent, providing a physiological signature of a cognitive process that was implemented under executive control. We found also that neural signals coding rule-dependent categories were distributed between the parietal and prefrontal cortex- however, not equally. Rule-dependent category signals were stronger, more powerfully modulated by the rule, and earlier to emerge in prefrontal cortex relative to parietal cortex. This suggests that prefrontal cortex may initiate the switch in neural representation at a network level that is important for computational flexibility.