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An algebraic formalism, developped with V. Glaser and R. Stora for the study of the generalized retarded functions of quantum field theory, is used to prove a factorization theorem which provides a complete description of the generalized retarded functions associated with any tree graph. Integrating over the variables associated to internal vertices to obtain the perturbative generalized retarded functions for interacting fields arising from such graphs is shown to be possible for a large category of space-times.