Flow cytometric histograms frequently consist of several components that show various degrees of overlap. For many types of analysis it is of great importance to decompose the original histogram into its components. To that purpose, we investigated the maximum likelihood approach in detail. It is shown that the iterative method to solve the maximum likelihood equations is well behaved for a variety of initial values. Algorithms to obtain initial values are presented, and the performance of the method is tested when applied to the analysis of DNA measurements from heterogeneous cell populations that differ with respect to DNA content.