The invention relates to a cosmetic composition comprising: (i) one or more products (A) of the reaction of: (a) one or more oxirane or oxetane compounds comprising at least two oxirane or oxetane groups and (b) one or more aminosilanes corresponding to the formula (1a): N(H)(R1)R2Si(OR3)3-a-b-c(OR4)a(R5Si(OR6)d(R7)e)bR8c (1a) in which: R1 is selected from the group constituted by H or a monovalent hydrocarbon-based radical comprising from 1 to 20 carbon atoms R2 is selected from the group constituted by a divalent, linear or branched, hydrocarbon-based radical, comprising from 1 to 60 carbons R4 is a hydrocarbon-based radical containing 3 to 200 carbon atoms R5 is selected from the group constituted by oxygen or a divalent, linear or branched, hydrocarbon-based radical comprising from 1 to 60 carbons R3, R6, R7 and R8 are each independently selected from the group constituted by monovalent, linear or branched, hydrocarbon-based radicals having from 1 to 200 carbon atoms the sub-script b is equal to zero or is a positive number and has a value ranging from 0 to 3 the subscript a is equal to zero or is a positive number below 3, the subscripts b and c are equal to zero or are positive and have a value ranging from 0 to 3 on condition that (a+b+c)<3 the subscripts d and e are equal to zero or are positive and have a value ranging from 0 to 3 on condition that (d+e)=3 and (ii) one or more acrylic thickening polymers. The invention also relates to a cosmetic method for treating keratin materials with this composition, and also to the use of this composition for caring for keratin materials.