Process for the preparation of polyesters and copolyesters by polycondensation of polyester-forming starting components, esters or oligoesters being prepared in a first reaction stage and subjected to polycondensation in a second reaction stage in the presence of titanium catalysts, wherein, in the polycondensation stage, at least one of a titanium dioxide/silicon dioxide coprecipitate having a composition of TiO.sub.2 :SiO.sub.2 =90:10 to 20:80 mol/mol and a titanium dioxide/zirconium dioxide coprecipitate having a composition of TiO.sub.2 :ZrO.sub.2 =95:5 to 70:30 mol/mol, which at least one coprecipitate is obtained by hydrolytic precipitation of metal alcoholates corresponding to each component of the coprecipitate and formed from monohydric or polyhydric alcohols, is employed as the polycondensation catalyst for polycondensation of the esters or oligoesters.