Introduction: Debilitating Long-Covid symptoms occur frequently after SARS-COVID-19 infection. Methods: Functional MRI was acquired in 10 Long Covid (LCov) and 13 healthy controls (HC) with a 7 Tesla scanner during a cognitive (Stroop color-word) task. BOLD time series were computed for 7 salience and 4 default-mode network hubs, 2 hippocampus and 7 brainstem regions (ROIs). Connectivity was characterized by the correlation coefficient between each pair of ROI BOLD time series. We tested for HC versus LCov differences in connectivity between each pair of the 20 regions (ROI-to-ROI) and between each ROI and the rest of the brain (ROI-to-voxel). For LCov, we also performed regressions of ROI-to-ROI connectivity with clinical scores. Results: Two ROI-to-ROI connectivities differed between HC and LCov. Both involved the brainstem rostral medulla, one connection to the midbrain, another to a DM network hub. Both were stronger in LCov than HC. ROI-to-voxel analysis detected multiple other regions where LCov connectivity differed from HC located in all major lobes. Most, but not all connections, were weaker in LCov than HC. LCov, but not HC connectivity, was correlated with clinical scores for disability and autonomic function and involved brainstem ROI. Discussion: Multiple connectivity differences and clinical correlations involved brainstem ROIs. Stronger connectivity in LCov between the medulla and midbrain may reflect a compensatory response. This brainstem circuit regulates cortical arousal, autonomic function and the sleep–wake cycle. In contrast, this circuit exhibited weaker connectivity in ME/CFS. LCov connectivity regressions with disability and autonomic scores were consistent with altered brainstem connectivity in LCov.