Data from longitudinal studies in which an initiating event and a subsequent event occur in sequence are called doubly censored data if the time of both events is interval-censored. In some cases, the second event also suffers left-truncation. This article is concerned with using doubly censored and truncated data to estimate the distribution function F of the duration time, i.e. the elapsed time between the originating event and the subsequent event. An iterative procedure is proposed to obtain the estimate of F. A simulation study is conducted to investigate the performance of the proposed estimator. A modified data set is used to illustrate the proposed approach.