Objectives Little is known about the aetiology of the links between sleep disturbance and anxiety and depression symptoms. The aim of this study was to estimate genetic and environmental influences on these associations. Methods Questionnaires were completed by 1556 young adults from twin and sibling pairs (61.5% female). Results Sleep disturbance was moderately correlated with symptoms of anxiety (r=.39) and depression (r=.50). There was substantial overlap between genes influencing sleep disturbance and those influencing symptoms of anxiety (rA=.58) and depression (rA=.68). Overall, the associations between sleep and symptoms of both anxiety and depression were mainly due to genes (explaining 74% and 58% of the covariances respectively), with the remainder due to nonshared environmental factors. Conclusions Moderate phenotypic and genetic correlations between the phenotypes support the view that sleep disturbance is related to the presence of various psychiatric difficulties, but also warrants independent consideration and treatment.