Process for the enhanced recovery of oil comprising introducing into an injection fluid at least one linear or structured water-soluble copolymer obtained by polymerization of 2-acrylamido-2-methylpropane sulfonic acid monomer in free acid and/or salified form with acrylamide derivative monomers having the formula H2C═CR—C(═O)-A in which R is H or CH3 or CH2COOR′, wherein R′ is an alkyl containing not more than 3 carbon atoms, and A is selected from the group consisting of 2-pyrrolidone, pyrrolidine and 4-morpholine, and injecting the injection fluid, which is then viscosified, into a reservoir, and thereafter recovering the aqueous and oily and/or gaseous mixture.