Background During the last decades, the prevalence of obesity [body mass index (BMI): weight/height(2)), >= 30.00 kg/m(2)] among adults has increased considerably. We examined whether this increase in a high-income, welfare state, like Denmark was driven by age, period or cohort effects, which would inform preventive strategies aiming at reducing the prevalence. Methods We used data from the National Representative Health and Morbidity Studies, which are representative surveys of the Danish adult population (age 16 years and above), conducted in 1987, 1994, 2000, 2005, 2010, 2013, 2017 and 2021 (N = 91 684). Participants reported height and weight, from which BMI was calculated after correction for systematic bias in self-reported data and non-response. Age, survey year and birth cohorts were mutually adjusted and adjusted for sex in generalized linear models. Results The obesity prevalence increased from 6.1% in 1987 to 18.4% in 2021, similarly in men (18.8%) and women (18.0%) and in all age groups. Age had an inverted u-shaped effect on the prevalence. Compared with individuals aged 16-24 years, the highest rate of obesity was seen for the age group 55-64 years [rate ratio 3.27, 95% confidence interval (CI): 2.58; 4.14]. The increasing rate for each recent survey year over time was compatible with a period effect without any birth cohort effects. The rate for obesity in 2021 was 4.16 in 1987 vs. 1987 (95% CI: 3.10; 5.59). Conclusions Obesity prevalence in Denmark increased steadily during the period 1987 through 2021, primarily driven by secular changes over time across all ages and birth cohorts.