The invention concerns modified hydrophobic polyelectrolytes by amide formation of a hydrophilic skeleton by n-alkylamines whereof the alkyl chain comprises 6 to 22 carbon atoms. Preferably, the amide formation is obtained by di-n-dodecylamine. The hydrophilic skeleton is preferably a sodium polyacrylate or polyacrylic acid corresponding to a statistical acrylate-AMPS copolymer. Said polymers can be used for stabilizing direct or invert emulsions likely to be destabilized or inverted by a modification in the degree of salinity of the aqueous phase or a pH modification. The invention is particularly useful for stabilizing oil drilling fluids or the like in particular drilling, fracturation, acidification or completion fluids.