Method for producing a comb-shaped copolymer whose skeleton is of an acrylamide, acrylic acid, acryloyl aminoethanol or dimethyl acrylamide type and on which poly(N-alkyl acrylamide) or poly(N,N-5 dialkyl acrylamide lateral segments are grafted, includes (a) producing a telomer poly(N-alkyl acrylamide) or poly(N,N-dialkyl acrylamide) of formula (I) H2N—R1-Z-{CH2—C(R2) [C(═O)N(R3) (R4)]—}n—H (I) 10 by reacting in water a compound of formula (II) CH2═C(R2)—C(═O)—N(R3) (R4) (II) with a chain limiting compound of formula (III) Z-R1—NH2; (b) isolating the telomer of formula (I) obtained at a stage (a); (c) reacting in water the telomer of formula (I) obtained at stage (b) with an acid chloride of formula (IV) CH2═C(R5)—C(═O)—C1 at a molar ratio (IV)/(III) equal to or less than 10 and equal to or greater than 1 so that a macro monomer of formula (V) 20 CH2═C(R5)—C(═O)NH—R1-Z-{CH2—C(R2) [C(═O)N(R3) (R4)]—}n—H (V) is obtained; (d) isolating the macro monomer of formula (V) obtained at stage (c); (e) copolymerizing in water the macro monomer of formula (V) isolated at stage (d) with a monomer selected from acrylamide, acrylic acid, acryloyl-aminoethanol or dimethyl-acrylamide and, if necessary, (f) purifying the thus obtained copolymer.