Polyesters such as polyethylene, polypropylene and polybutylene terephthalate are made from melts of precondensates of polyesters by first conducting vapors comprising precondensate components distributed in the form of an aerosol through a polycondensation reactor in which precondensate components are deposited on the reactor wall and in an outlet chamber of the reactor on a separator. Then the deposits are conducted to the unstirred discharge sump. Upper layers of the discharge sump are continuously recirculated in the stirred reactor area and thus subjected to reconversion and further polycondensation.