Abstract: This paper presents optimum plans of simple constant-stress accelerated life tests with com peting causes of failure which life distribution of each failure cause is assumed to be exponential.We obtain the optimum test design to minimize the sum of asyniptotie vaeiance of the Maximum Likelihood Estimation （MLE） of the mean life in each cause at a design stress.A series of mter esting results are shown,which are similar to or identical with those results shown in a lot of other papers.