Aims: To apply item response mixture modelling (IRMM) to investigate the viability of the dimensional and categorical approaches to conceptualizing alcohol and cannabis use disorders. Design: A cross-sectional survey assessing substance use and DSM-IV substance use disorders. Setting and participants: A household survey of a nationally representative sample of 10 641 Australia adults (aged 18 years or older). Measurements: Trained survey interviewers administered a structured interview based on the Composite International Diagnostic Interview (CIDI). Findings: Of the 10 641 Australian adults interviewed, 7746 had drunk alcohol in the past 12 months and 722 had used cannabis. There was no improvement in fit for categorical latent class nor mixture models combining continuous and categorical parameters compared to continuous factor analysis models. The results indicated that both alcohol and cannabis problems can be considered as dimensional, with those with the disorder arrayed along a dimension of severity. Conclusions: A single factor accounts for more variance in the DSM-IV alcohol and cannabis use criteria than latent class or mixture models, so the disorders can be explained most effectively by a dimensional score.