The invention relates to a block polymer comprising: a first block with a glass transition temperature (Tg) of greater than or equal to 40° C., obtained from a monomer CH2═C(R1)—COOR2, in which R1═H or methyl, R2═C4 to C12 cycloalkyl group and a second block with a glass transition temperature (Tg) of less than or equal to 20° C. derived from a vinylphosphonic acid and from a monomer CH2═C(R1)—COOR3, in which R1═H or methyl, R3=linear or branched C1 to C6 unsubstituted alkyl group, with the exception of a tert-butyl group or a methoxyethyl group. The invention also relates to a cosmetic composition comprising such a block polymer, and also to a process for caring for or making up keratin materials using said block polymer combined with an additional compound chosen from polyamine compounds bearing several primary amine groups and/or secondary amine groups, amino alkoxysilanes, salts of divalent or trivalent metal ions, clays and metal oxides. The process makes it possible to obtain a film-forming deposit that has good resistance to water, to oil and to sebum. The film is also non-tacky and transfer-resistant.
