Background: Previous studies have suggested a bidirectional association between sleep problems and anxiety symptoms in adolescents. These studies used methods that do not separate between-person effects from within-person effects, and therefore their conclusions may not pertain to within-person mutual influences of sleep and anxiety. We examined bidirectional associations between sleep problems and anxiety during adolescence and young adulthood while differentiating between person effects from within-person effects. Methods: Data came from the Dutch TRacking Adolescents' Individual Lives Survey (TRAILS), a prospective cohort study including six waves of data spanning 15 years. Young adolescents (N = 2230, mean age at baseline 11.1 years) were followed every 2–3 years until young adulthood (mean age 25.6 years). Sleep problems and anxiety symptoms were measured by the Youth Self-Report, Adult Self-Report and Nottingham Health Profile. Temporal associations between sleep and anxiety were investigated using the random intercept cross-lagged panel model. Results: Across individuals, sleep problems were significantly associated with (β = 0.60, p < 0.001). At the within-person level, there were significant cross–sectional associations between sleep problems and anxiety symptoms at all waves (β = 0.12–0.34, p < 0.001). In addition, poor sleep predicted greater anxiety symptoms between the first and second, and between the third and fourth assessment wave. The reverse association was not statistically significant. Conclusions: Within-person associations between sleep problems and anxiety are considerably weaker than between-person associations. Yet, our findings tentatively suggest that poor sleep, especially during early and mid-adolescence, may precede anxiety symptoms, and that anxiety might be prevented by alleviating sleep problems in young adolescents.