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Background Whether the reported high risk of age-related diseases in HIV-infected people is caused by biological ageing or HIV-associated risk factors such as chronic immune activation and low-grade infl ammation is unknown. We assessed time trends in age-standardised and relative risks of nine serious age-related diseases in a nationwide cohort study of HIV-infected individuals and population controls. Methods We identifi ed all HIV-infected individuals in the Danish HIV Cohort Study who had received HIV care in Denmark between Jan 1, 1995, and June 1, 2014. Population controls were identifi ed from the Danish Civil Registration System and individually matched in a ratio of nine to one to the HIV-infected individuals for year of birth, sex, and date of study inclusion. Individuals were included in the study if they had a Danish personal identifi cation number, were aged 16 years or older, and were living in Denmark at the time of study inclusion. Data for study outcomes were obtained from the Danish National Hospital Registry and the Danish National Registry of Causes of Death and were cardiovascular diseases (myocardial infarction and stroke), cancers (virus associated, smoking related, and other), severe neurocognitive disease, chronic kidney disease, chronic liver disease, and osteoporotic fractures. We calculated excess and agestandardised incidence rates and adjusted incidence rate ratios of outcomes for time after HIV diagnosis, highly active antiretroviral therapy (ART) initiation, and calendar time. The regression analyses were adjusted for age, sex, calendar time, and origin. Findings We identifi ed 5897 HIV-infected individuals and 53 073 population controls; median age was 36.8 years (IQR 30.6-44.4), and 76% were men in both cohorts. Dependent on disease, the HIV cohort had 55 050-57 631 person-years of follow-up and the population controls had 638 204-659 237 person-years of follow-up. Compared with the population controls, people with HIV had high excess and relative risk of all age-related diseases except other cancers. Overall, the age-standardised and relative risks of cardiovascular diseases, cancers, and severe neurocognitive disease did not increase substantially with time after HIV diagnosis or ART initiation. Except for chronic kidney diseases, the age-standardised and relative risks of age-related diseases did not increase with calendar time. Interpretations Severe age-related diseases are highly prevalent in people with HIV, and continued attention and strategies for risk reduction are needed. The fi ndings from our study do not suggest that accelerated ageing is a major problem in the HIV-infected population. Funding Preben og Anna Simonsens Fond, Novo Nordisk Foundation, Danish AIDS Foundation, Augustinus Foundation, and Odense University Hospitals Frie Fonds Midler.