When melt‐extruded in the presence of triphenylphosphite (TPP), the molecular weight of polyesters such as poly(ethylene terephthalate) (PET) increases with time. Analysis of the PET chain end groups and model studies of high‐temperature reactions indicate that, most likely, the process leading to chain extension of PET in the presence of TPP takes place in two steps. In the first step, TPP rapidly reacts with the hydroxyl end groups by displacing one phenoxy group from the TPP. In the second step, a slow reaction takes place between the alkyldiphenyl phosphite and carboxylic chain end groups, forming an ester bond between the carboxyl and alkyl groups, and producing diphenylphosphite (DPP) as a reaction by‐product. The DPP tautomerizes to its pentacovalently bonded stabler form of diphenylphosphate, the form in which the DPP was usually detected in our analyses. The ester formation results in the extension of the PET chains. Model studies are presented which support the proposed mechanism.