Abstract: The composition for permanent shaping of hair based on a hair keratin-reducing agent contains N-glycyl-L-cysteine and/or L-cysteinyl-glycine as the hair keratin-reducing agent. The N-glycyl-L-cysteine and/or L-cysteinyl-glycine is advantageously the only hair keratin-reducing substance present. The compositions have a preferred pH range of 6.5 to 9.0 and contain from 8 to 30 percent by weight of the N-glycyl-L-cysteine and/or L-cysteinyl-glycine. Use of this composition for permanent shaping of hair avoids a troublesome white deposit or coating on the hair which occurs when cysteine-containing hair shaping compositions are used.