stochastic exponential; chaotic representation. Abstract. This paper derives several identities for the iterated integrals of a general semimartingale. They involve powers, brackets, exponential and the stochastic exponen-tial. Their form and derivations are combinatorial. The formulae simplify for continuous or finite-variation semimartingales, especially for counting processes. The results are mo-tivated by chaotic representation of martingales, and a simple such application is given.