Hair treatment process using a composition comprising: - at least one organic solvent, - less than 2% by weight of water relative to the total weight of the composition, - one or more polymers containing silicone units and bearing alkoxy-(aminomethyl)-silyl functional groups of formula below: in which: - Z 2 represents a group -CH 2 -NR 3 R 4; - Z 3 represents a group OR 5 or R 6; - R 3, which may be identical or different, represent a hydrogen atom or a group R 7; - R 1, R 5, R 6 and R 7, which may be identical or different, represent a C 1 -C 6 alkyl group and R 4 represents a C 1 -C 6 alkyl group or a C 5 -C 6 cycloalkyl group; R 3 and R 4 possibly forming, with the nitrogen atom that bears them, a 5- to 8-membered heterocycle comprising from 1 to 3 heteroatoms, R a and R b, which may be identical or different, represent a C 1 -C 2 alkyl group, n ranges from 5 to 1000 in which SiR a R b -[OSiR a R b]n- of formula is a unit derived from a linear silicone with a weight-average molecular mass (Mw) ranging from 400 to 25 000, the polymer(s) containing silicone units and bearing alkoxy-(aminomethyl)-silyl functional groups, of formula, represent from 0.5% to 30% by weight relative to the total weight of the composition. - at least one organic solvent, - less than 2% by weight of water relative to the total weight of the composition, - one or more polymers containing silicone units and bearing alkoxy-(aminomethyl)-silyl functional groups of formula below: in which: - Z 2 represents a group -CH 2 -NR 3 R 4; - Z 3 represents a group OR 5 or R 6; - R 3, which may be identical or different, represent a hydrogen atom or a group R 7; - R 1, R 5, R 6 and R 7, which may be identical or different, represent a C 1 -C 6 alkyl group and R 4 represents a C 1 -C 6 alkyl group or a C 5 -C 6 cycloalkyl group; R 3 and R 4 possibly forming, with the nitrogen atom that bears them, a 5- to 8-membered heterocycle comprising from 1 to 3 heteroatoms, R a and R b, which may be identical or different, represent a C 1 -C 2 alkyl group, n ranges from 5 to 1000 in which SiR a R b -[OSiR a R b]n- of formula is a unit derived from a linear silicone with a weight-average molecular mass (Mw) ranging from 400 to 25 000, the polymer(s) containing silicone units and bearing alkoxy-(aminomethyl)-silyl functional groups, of formula, represent from 0.5% to 30% by weight relative to the total weight of the composition. - Z 2 represents a group -CH 2 -NR 3 R 4; - Z 3 represents a group OR 5 or R 6; - R 3, which may be identical or different, represent a hydrogen atom or a group R 7; - R 1, R 5, R 6 and R 7, which may be identical or different, represent a C 1 -C 6 alkyl group and R 4 represents a C 1 -C 6 alkyl group or a C 5 -C 6 cycloalkyl group; R 3 and R 4 possibly forming, with the nitrogen atom that bears them, a 5- to 8-membered heterocycle comprising from 1 to 3 heteroatoms, R a and R b, which may be identical or different, represent a C 1 -C 2 alkyl group, n ranges from 5 to 1000 in which SiR a R b -[OSiR a R b]n- of formula is a unit derived from a linear silicone with a weight-average molecular mass (Mw) ranging from 400 to 25 000, the polymer(s) containing silicone units and bearing alkoxy-(aminomethyl)-silyl functional groups, of formula, represent from 0.5% to 30% by weight relative to the total weight of the composition.