Method for thickening a cosmetic formulation, through the contact of said formulation with a direct aqueous emulsion of a polymer, followed by pH regulation at a value between 5 and 7, preferably between 5 and 6.5, most preferably between 5, 5 and 6, characterized in that the emulsion is free of organic surfactants and solvents other than water, and that said polymer consists, expressed in% by weight of each of the monomers: a) from 20% to 60% by weight of methacrylic acid and acrylic acid, b) from 40% to 80% by weight of at least one monomer selected from ethyl acrylate, butyl acrylate, methyl methacrylate and mixtures thereof, c) from 0.05% to 22% by weight of acid 2-acrylamido-2-methylpropanesulfonic acid, d) from 0 to 1% by weight of at least one crosslinking monomer, the total of a) + b) + c) + d) is equal to 100%, or a) of 20% at 60% by weight of methacrylic acid and acrylic acid, b) from 40% to 80% by weight of at least one monomer chosen from acr ethyl ilate, butyl acrylate, methyl methacrylate and mixtures thereof, c) from 0.5% to 25% by weight of a monomer containing a hydrophobic group, d) from 0.05% to 22% by weight of acid 2-acrylamido-2-methylpropanesulfonic acid, e) from 0 to 1% by weight of at least one crosslinking monomer, the total of a) + b) + c) + d) + e) is equal to 100%, the% in Acrylic acid weight compared to the total weight of acrylic and methacrylic acids is between 50% and 100%, preferably between 80% and 100%, most preferably between 98% and 100% and extremely preferably where This percentage (%) is equal to 100%.Procedimiento para espesar una formulación cosmética, a través del contacto de dicha formulación con una emulsión acuosa directa de un polímero, seguido de la regulación del pH a un valor entre 5 y 7, preferentemente entre 5 y 6,5, muy preferentemente entre 5,5 y 6, caracterizado porque la emulsión está exenta de tensioactivos y disolventes orgánicos distintos del agua, y porque dicho polímero consiste, expresado en % en peso de
