Flexible changes in behavior can involve changes in the processing of external information (i.e., shifts in attention between different stimuli) or internal information (i.e., shifts in task rules stored in memory). However, it is unclear if different types of flexible change rely on separate, domain-specific neural processes or on a domain-general system, which enables flexible actions independent of the type of change needed. In the current study, participants performed a task switching procedure while we measured neural oscillations via EEG. Importantly, we independently manipulated the need to switch attention between 2 types of stimuli, as well as the need to switch between two sets of stimuli-response rules stored in memory. Both attentional and rule switches significantly increased error rates and RTs. On a neural level, both types of changes were associated with a widespread decrease in alpha power, predominantly over the parietal cortex. Attentional switches and rule switches showed a subadditive interaction effect on both participants’ performance as well as on their alpha power reactivity. This indicates that implementing both changes at the same time was more efficient than implementing each individual change separately. Independent of the presence or absence of either attentional or rule switches, higher frontal theta power and lower parietal/posterior alpha power predicted faster responses on correct trials. Our study suggests that flexible behavior relies on domain-general frontal and parietal oscillatory dynamics, which enable efficient implementation of goal-directed actions independent of which aspects of the task change.