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INTRODUCTION: We investigated the potential association of COVID-19 vaccination with three acute neurological events: Guillain-Barré syndrome (GBS), transverse myelitis and Bell's palsy. METHODS: With the approval of NHS England we analysed primary care data from >17 million patients in England linked to emergency care, hospital admission and mortality records in the OpenSAFELY platform. Separately for each vaccine brand, we used a self-controlled case series design to estimate the incidence rate ratio for each outcome in the period following vaccination (4-42 days for GBS, 4-28 days for transverse myelitis and Bell's palsy) compared to a within-person baseline, using conditional Poisson regression. RESULTS: Among 7,783,441 ChAdOx1 vaccinees, there was an increased rate of GBS (N = 517; incidence rate ratio 2·85; 95% CI2·33-3·47) and Bell's palsy (N = 5,350; 1·39; 1·27-1·53) following a first dose of ChAdOx1 vaccine, corresponding to 11.0 additional cases of GBS and 17.9 cases of Bell's palsy per 1 million vaccinees if causal. For GBS this applied to the first, but not the second, dose. There was no clear evidence of an association of ChAdOx1 vaccination with transverse myelitis (N = 199; 1·51; 0·96-2·37). Among 5,729,152 BNT162b2 vaccinees, there was no evidence of any association with GBS (N = 283; 1·09; 0·75-1·57), transverse myelitis (N = 109; 1·62; 0·86-3·03) or Bell's palsy (N = 3,609; 0·89; 0·76-1·03). Among 255,446 mRNA-1273 vaccine recipients there was no evidence of an association with Bell's palsy (N = 78; 0·88, 0·32-2·42). CONCLUSIONS: COVID-19 vaccines save lives, but it is important to understand rare adverse events. We observed a short-term increased rate of Guillain-Barré syndrome and Bell's palsy after first dose of ChAdOx1 vaccine. The absolute risk, assuming a causal effect attributable to vaccination, was low.