In a process for the continuous preparation of polymers with repeating succinyl units, maleic anhydride or a derivative thereof as educt A is mixed with ammonia or an ammonia-producing compound or amides of carbonic acid as educt B and in a first reaction stage these are reacted to give an N-containing low molecular derivative of maleic acid. This derivative is then polymerized in a subsequent second reaction stage. Reaction of the educts (A,B) takes place largely adiabatically in the first reaction stage. The heat of reaction thereby released is used to take the reaction mixture to the polymerization temperature and in the second reaction stage at least partially to polymerize the N-containing low molecular derivative to obtain a polymer with repeating succinyl units.