Abstract: Disclosed is an improvement in a process for producing branched polyesters wherein a precursor polyester is first formed and subsequently the precursor polyester is formed into particles and further polymerized in the solid state, wherein the improvement comprises contacting the particles while at a temperature of about 140.degree. to about 2.degree. C. below the melting point of the polyester with the vapor of water or an organic compound having at least one OH group.