A process for separating acrylic acid present as a main product and glyoxal present as a by-product in a product gas mixture of a partial gas phase oxidation of a C.sub.3 precursor compound, in which a liquid phase P is obtained, which consists of acrylic acid to an extent of at least 70% of its weight and, based on the molar amount of acrylic acid present therein, comprises at least 200 molar ppm of glyoxal, in which the glyoxal is separated from the acrylic acid in the liquid phase P by crystallization.