Hierarchically organized brains communicate through feedforward (FF) and feedback (FB) pathways. In mammals, FF and FB are mediated by higher and lower frequencies during wakefulness. FB is preferentially impaired by general anesthetics in multiple mammalian species. This suggests FB serves critical functions in waking brains. The brain of Drosophila melanogaster (fruit fly) is also hierarchically organized, but the presence of FB in these brains is not established. Here, we studied FB in the fly brain, by simultaneously recording local field potentials (LFPs) from low-order peripheral structures and higher-order central structures. We analyzed the data using Granger causality (GC), the first application of this analysis technique to recordings from the insect brain. Our analysis revealed that low frequencies (0.1–5 Hz) mediated FB from the center to the periphery, while higher frequencies (10–45 Hz) mediated FF in the opposite direction. Further, isoflurane anesthesia preferentially reduced FB. Our results imply that the spectral characteristics of FF and FB may be a signature of hierarchically organized brains that is conserved from insects to mammals. We speculate that general anesthetics may induce unresponsiveness across species by targeting the mechanisms that support FB.