Oil-in-water type emulsions having a pH below or equal to 3.5, especially a pH below or equal to 3, and comprising as a stabilizing agent a substantially water-soluble crosslinked anionic copolymer consisting of units derived from the reaction between (i) acrylamide, (ii) 2-acrylamido-2-methylpropanesulfonic acid and (iii) at least one compound possessing multiple olefinic unsaturation (crosslinking agent), in which the compound possessing multiple olefinic unsaturation is present in the copolymer at a concentration of between 0.06 and 1 mmol per mole of the collective monomer units, are stable.