Process for inhibiting the undesired free-radical polymerization of acrylic acid present in a liquid phase P, wherein the acrylic acid content of P is at least 10% by weight, the liquid phase P comprises in the range from 25 to 1000 ppmw of glyoxal based on the weight of the acrylic acid present in P and the liquid phase P is admixed with furfural in an amount that results in a furfural content in the range from 25 to 1000 ppmw based on the weight of the acrylic acid present in P. Liquid phase P, wherein the acrylic acid content of P is at least 10% by weight and the liquid phase P comprises in the range from 25 to 1000 ppmw of glyoxal and in the range from 25 to 1000 ppmw of furfural in each case based on the weight of the acrylic acid present in P.