A general ‘successive substitutions’ scheme is developed to estimate parameters in a finite mixture of distributions from the exponential family, based on censored data. It is assumed that the data can be grouped in the first class and the number of observations in each of the remaining classes are known. Examples from Poisson, Exponential and Normal distributions are given. A small simulation exercise has also been carried out for the mixture of two one - parameter exponential population. © 1987, Taylor & Francis Group, LLC. All rights reserved.