The invention relates to a method for producing acrylic acid and methacrylic acid by producing a gaseous product mixture which essentially has the composition of a reaction mixture of the catalytic gas phase oxidation of C3-/C4- alkanes, -alkenes, -alkanols or -alkanals or precursors thereof to form acrylic acid or methacrylic acid. The product is separated from the gaseous product mixture according to a method comprising the following steps: a) condensing the gaseous product mixture; b) crystallising the acrylic acid or methacrylic acid from the solution obtained in (a); c) separating the resulting crystals from the mother liquor and d) returning at least a part of the mother liquor from stage (c) to stage (a).