Summary: The EM algorithm concerns maximum likelihood estimation for incomplete data. We present a simulated annealing type EM algorithm: SAEM. This algorithm is an adaptation of the stochastic EM algorithm (SEM) that we have previously developed [see Rev. Stat. Appl. 34, No.2, 35-52 (1986)]. Like SEM, SAEM overcomes most of the well-known limitations of EM. Moreover, SAEM performs better for small samples. Here, we focus on the mixture problem. We state a theorem which asserts that each SAEM sequence converges a.s. to a local maximizer of the likelihood function.