The present invention relates to a hair-shaping composition suitable for topical application to the hair, wherein the composition has a pH of 4 or less and comprises, in an aqueous continuous phase, (i) (based on the total weight of the composition ) At least 0.5% by weight of one or more polyhydroxy acid lactones (ii) at least 0.5% by weight (based on the total weight of the composition) of one or more aliphatic dicarboxylic acids or tricarboxylic acids, and (Iii) at least 0.1% by weight (based on the total weight of the composition) of glyoxylic acid or a salt thereof or a hydrate thereof.本発明は、毛髪への局所適用に適した毛髪成形組成物であって、この組成物が4以下のpHを有し、水性連続相中に、(i)(組成物の総重量に基づいて)少なくとも0.5重量%の1つ以上のポリヒドロキシ酸ラクトン;(ii)(組成物の総重量に基づいて)少なくとも0.5重量%の1つ以上の脂肪族ジカルボン酸またはトリカルボン酸、および(iii)(組成物の総重量に基づいて)少なくとも0.1重量%のグリオキシル酸またはその塩またはその水和物を含む組成物を提供する。
