The invention concerns a polyester bearing tertiary carboxyl groups, characterised in that it consists of: (a) 8.1 to 35 moles of an aliphatic or cycloaliphatic of a polyol; (b) 9.1 to 36 moles of an aliphatic, cycloaliphatic or aromatic polycarboxylic acid; (c) 1.6 to 2.8 moles of an aliphatic, cycloaliphatic or aromatic compound comprising a tertiary carboxyl group and either a primary or secondary carboxyl group, or a primary or secondary hydroxyl group. Said polyester is prepared in several steps, the first steps consisting in the preparation of a polyester by condensation between (a) an aliphatic or cycloaliphatic polyol, and (b) an aliphatic, cycloaliphatic or aromatic polycarboxylic acid, the final step consisting in condensing said polyester with (c) an aliphatic, cycloaliphatic or aromatic compound comprising a tertiary carboxyl group and either a primary or secondary carboxyl group, or a primary or secondary hydroxyl group. Said polyester is used in thermosetting powder compositions, mixed with a crosslinking agent which is more particularly a &bgr;-hydroxylalkylarnide. Said compositions provide coatings with excellent surface appearance, good flexibility and good resistance to poor weather conditions.