Thermoplastic polyesters having a melt viscosity of more than 6,000 poise, as measured at 250.degree. C, and a relative solution viscosity of more than 1.6, as measured on a 2:1 mixture of phenol/o-dichlorobenzene at 25.degree. C, composed of aliphatic and/or cycloaliphatic diols on the one hand and dicarboxylic acids or esters thereof on the other hand and of from 0.1 to 10% molar of an aliphatic diol containing at least one olefinic double bond and/or of an aliphatic dicarboxylic acid containing at least one olefinic double bond or an ester thereof, said olefinic double bond not being directly adjacent to the carboxyl or ester groups. The polyesters are manufactured by melt polycondensation of diols with dicarboxylic acids or esters thereof, which polycondensation is carried out for at least some of the time at a temperature above 220.degree. C and preferably above 230.degree. C, the reaction being carried out in the presence of from 0.1 to 10% molar of an aliphatic diol containing at least one olefinic double bond and/or of an aliphatic dicarboxylic acid containing at least one olefinic double bond or an ester thereof, said olefinic double bond not being directly adjacent to the carboxyl or ester groups.