Sleep problems in adolescence are increasingly common, and associated with adverse health and psychological outcomes. Adolescents' sleep problems may be related to the family's socioeconomic status, but studies are few and no study has examined whether social inequality in sleep problems changes as sleep problems become increasingly common. This study examined trends in difficulties falling asleep among adolescents in Denmark, whether this sleep problem was associated with socioeconomic status, and whether this association changed from 1991 to 2018. The study applied data from eight comparable surveys among 11-15 year olds in Denmark 1991-2018, the Danish arm of the international Health Behaviour in School-aged Children study, N = 30,002. The prevalence of daily difficulties falling asleep increased from 7.0% to 13.4% in 1991-2018 with higher frequencies among girls and younger adolescents. The odds ratio (95% confidence interval) for daily difficulties was 1.14 (1.05-1.24) in middle and 1.52 (1.37-1.69) in low compared with high socioeconomic status. The absolute social inequality in difficulties falling asleep was persistent in 1991-2018 whereas the relative social inequality may have decreased. The increasing prevalence and the social inequality in difficulties falling asleep among adolescents is a serious public health concern that calls for more attention and efforts.