The EM-algorithm assures monotone increase of the incomplete data likelihood, but does not in general guarantee convergence of the parameter estimates. We take a fresh look at the situation and present sufficient conditions for convergence that are conveniently verifiable in practical situations. Illustrations with typical applications of the EM-algorithm are given. Key words: Kullback-Leibler divergence, Fisher information, exponential family, proximal point method, definability, information geometry