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Summary: Background: Adverse events of special interest (AESIs) were pre-specified to be monitored for the COVID-19 vaccines. Some AESIs are not only associated with the vaccines, but with COVID-19. Our aim was to characterise the incidence rates of AESIs following SARS-CoV-2 infection in patients and compare these to historical rates in the general population. Methods: A multi-national cohort study with data from primary care, electronic health records, and insurance claims mapped to a common data model. This study's evidence was collected between Jan 1, 2017 and the conclusion of each database (which ranged from Jul 2020 to May 2022). The 16 pre-specified prevalent AESIs were: acute myocardial infarction, anaphylaxis, appendicitis, Bell's palsy, deep vein thrombosis, disseminated intravascular coagulation, encephalomyelitis, Guillain- Barré syndrome, haemorrhagic stroke, non-haemorrhagic stroke, immune thrombocytopenia, myocarditis/pericarditis, narcolepsy, pulmonary embolism, transverse myelitis, and thrombosis with thrombocytopenia. Age-sex standardised incidence rate ratios (SIR) were estimated to compare post-COVID-19 to pre-pandemic rates in each of the databases. Findings: Substantial heterogeneity by age was seen for AESI rates, with some clearly increasing with age but others following the opposite trend. Similarly, differences were also observed across databases for same health outcome and age-sex strata. All studied AESIs appeared consistently more common in the post-COVID-19 compared to the historical cohorts, with related meta-analytic SIRs ranging from 1.32 (1.05 to 1.66) for narcolepsy to 11.70 (10.10 to 13.70) for pulmonary embolism. Interpretation: Our findings suggest all AESIs are more common after COVID-19 than in the general population. Thromboembolic events were particularly common, and over 10-fold more so. More research is needed to contextualise post-COVID-19 complications in the longer term. Funding: None.