In a process for the purification of acrylic acid or methacrylic acid by crystallization and distillation, the following steps are carried out: (a) crystallization of a mixture containing the acrylic acid or methacrylic acid with formation of product crystals having a higher concentration of acrylic acid or methacrylic acid and of a mother liquor, (b) distillation of at least part of the mother liquor from step (a) with formation of a distillation residue, which is at least partly removed, and of a top product, (c) crystallization of at least part of the top product from step (b) with formation of a crystallization residue, which is removed, and of crystals and (d) recycling of the crystals from step (c) to the crystallization (a).