The present invention relates to a kind of cosmetic composition, it includes: at least one of which keratin fiber conditioner One or more of polymer formulaes (I): in the accompanying drawings :-Z1 represents bivalent group-CH2-T or-T-CH2- T represents oxygen or sulphur atom, or a group is chosen from ever-increasing business operation N (R2), N-(R2) (I), C (zero)-N (R2), S- (CO), be expert at (CO), and o- (CO) and (CO) < - Z2 indicates group OR1 or R8-CH2-NR3R4 - Z3 indicates group OR5 or R6 - p1 is equal to 1 - p2 is equal to 0 or 1 - R2 and R3, can be identical or different, represents hydrogen atom or group R7 R1, R5, R6, R7 and R8, they can be identical or different, represents C1-C6, preferably C1-C2 alkyl C1-C6, the preferably preferred C6 naphthenic base of C1-C2 alkyl or C5-C6, such as cyclohexyl are indicated with R4 R3 and R4 may be optionally formed that has their 5-to 8- circle heterocyclic rings with nitrogen-atoms, contain the hetero atom from 1 to 3 W indicates diatomic polymer chain. The present invention also relates to use this composition in the technique and equipment for being with or without catalyst.