A process for the preparation of a polymer having recurring succinyl units comprising reaction of compound A, an unsaturated C.sub.4 -dicarboxylic acid or a derivative thereof, with compound B, a nitrogen-donating compound, in water in a first reaction step at a temperature of from 50 to 250.degree. C. to give a reaction mixture wherein the molar ratio of compound A to compound B is 1:1.5-25, and the water content of the reaction mixture is 35 to 95% by weight, based on the total reaction mixture, and further wherein at least 50% of compound A is reacted with compound B in said first reaction step, and subsequent to said first reaction step optionally continuously feeding the reaction mixture, without intermediate isolation, into an optionally continuously operated reactor, water being removed, and treatment of the reaction mixture at a temperature of 140 to 350.degree. C. in the reactor for a residence time of 0.5 minute to 48 hours to give the polymer having recurring succinyl units.