A process for the permanent reshaping of the hair comprising, in a first step, applying to said hair for a period of time ranging from approximately 5 to 60 minutes so as to reduce the disulfide linkages of said hair, a composition comprising
- (i) an effective amount of a compound having the formula
- HS--A--Y--B (I)
- wherein
- Y represents --COO-- or --NH-- and
- (a) when Y represents --COO--,
- A represents --(CH.sub.2).sub.n -- wherein n is 1 or 2 or ##STR4## wherein R represents linear or branched C.sub.1 -C.sub.3 alkyl, and B represents --H, --CH.sub.2 --CH.sub.2 OH, --CH.sub.2 --CHOH--CH.sub.2 OH, ##STR5## (b) when Y represent --NH--, A represents ##STR6## wherein R' represents methyl or ethyl, and B represents --H or, when A represents --CH.sub.2 --CH.sub.2 --, B also represents --CO--R" wherein R" represents linear or branched C.sub.1 -C.sub.4 alkyl, and
- (ii) a pulverulent malodorous compound removing absorbing agent which is insoluble in the composition and, when suspended in an aqueous solution containing 92 g/l of thioglycolic acid, the aqueous solution also contains at least 30 percent by weight of initial thioglycolic acid after contact for 15 minutes and,
- in a second step, reforming said disulfide linkages by applying thereto an oxidizing composition or by permitting atmosphere oxygen to act on said hair.