The invention relates to polymers with a mean molecular weight of between 500 and 500,000 g/mol that can be produced as follows: A) reaction of a compound of formula 1, in which n stands for 0, 1 or 2 and A for an arbitrarily substituted C1-C40 group with a compound of the formula 2 B(OH)m in which m is from 2 to 10 and B is a represents an arbitrarily substituted C2-C40 group, B) subsequently reaction of the product thus obtained with a nitrogen-containing carboxylic acid which comprises from 1 to 20 carbon atoms, where the molar ratio between the number of free OH groups of the polyester obtained in step A and the nitrogen-containing carboxylic acid is between 1:0.1 and 1:1. The polymers are used to inhibit gas hydrate formation.