jats:titleSummary</jats:title>jats:pThis paper provides methods to estimate finite mixtures from data with repeated measurements non-parametrically. We present a constructive identification argument and use it to develop simple two-step estimators of the component distributions and all their functionals. We discuss a computationally efficient method for estimation and derive asymptotic theory. Simulation experiments suggest that our theory provides confidence intervals with good coverage in small samples.</jats:p>