Abstract: The invention relates to a process for enhanced hydrocarbon recovery in a subterranean formation, in particular enhanced crude oil recovery, using at least one water-soluble terpolymer in aqueous solution, said water-soluble terpolymer being a partially hydrolysed polyacrylamide of formula (I) wherein X is an alkali metal cation chosen from sodium, lithium or potassium, or an ammonium cation NH4+; the coefficients a, b and c being defined in the following way: a a + b + c is greater than or equal to 0.50, preferably between 0.5 and 0.8, limits included, b a + b + c is less than 0.50, preferably between 0.1 and 0.4, limits included, c a + b + c is between 0.01 and 0.20, preferably between 0.02 and 0.15, limits included, all of the ratios having a sum equal to 1.