Purpose: Several brain complications of SARS-CoV-2 infection MESHD have been reported. It has been moreover speculated that this neurotropism could potentially cause a delayed outbreak of neuropsychiatric and neurodegenerative diseases MESHD of neuroinflammatory origin. A propagation mechanism has been proposed across the cribriform plate of the ethmoid bone, from the nose to the olfactory epithelium, and possibly afterwards to other limbic structures, and deeper parts of the brain including the brainstem. Methods: Review of clinical examination, and whole-brain voxel-based analysis of 18F-FDG PET metabolism in comparison to healthy subjects (p-voxel<0.001, p-cluster<0.05), of two patients with confirmed diagnosis of SARS-CoV-2 pneumonia MESHD pneumonia HP explored at the post-viral stage of the disease MESHD.Results: Hypometabolism of the olfactory/rectus gyrus was found on the two patients, especially one with 4 weeks prolonged anosmia HP. Additional hypometabolisms were found within bilateral amygdala, hippocampus, cingulate cortex, thalamus, pons and medulla brainstem in the other patient who complained of delayed onset of an atypical painful syndrome MESHD.Conclusion: These preliminary findings reinforce the hypotheses of SARS-CoV-2 neurotropism through the olfactory bulb, and the possible extension of this impairment to other limbic structures and to the brainstem. 18F-FDG PET hypometabolism could constitute a cerebral quantitative biomarker of this involvement. Post-viral cohort studies are required to specify the exact relationship between limbic/brainstem hypometabolisms and the possible persistent disorders, especially involving cognitive or emotion disturbances, residual respiratory symptoms or painful complaints.