Background: Little is known about changes of mental health during the COVID-19 pandemic in potentially disadvantaged groups. We investigated changes in anxiety and depression symptoms during the first year of the pandemic in six European countries and Australia by prior mental disorders and migration status. Methods: Overall, 4674 adults answered a web-based survey in May–June 2020 and were followed by three repeated surveys up to February 2021. Information on psychosocial, financial and demographic, living conditions, prior mental disorders, depression and anxiety symptoms during the pandemic and migration status was collected. Weighted general estimation equations modelling was used to investigate the association between prior mental disorders, migration status, and symptoms over time. Results: Most participants were <40 years old (48%), women (78%) and highly educated (62%). The baseline prevalence of depressive and anxiety symptoms ranged between 19%–45% and 13%–35%, respectively. In most countries, prevalence rates remained unchanged throughout the pandemic and were higher among people with prior mental disorders than without even after adjustment for several factors. We observed interactions between previous mental disorders and symptoms of anxiety or depression over time in two countries. No difference by migration status was noted. Limitations: Convenience sampling limits generalizability. Self-assessed symptoms of depression and anxiety might involve some misclassification. Conclusions: Depression and anxiety symptoms were worse among individuals with prior mental disorders than without, but there was no clear trend of worsening mental health in the observed groups during the observed period.