The invention provides a process for producing and/or purifying acrylic acid or methacrylic acid or an ester of any of these, wherein mixtures of high-boiling heavy ingredients (high-boiling matter mixtures) discharged from individual step units are classified by the content therein of (meth)acrylic acid and/or of the dimer thereof and handled. According to the invention, even when high-boiling matters which have been discharged from distillation columns, high-boiling-matter cracking reactors, and the like in a plant for producing (meth)acrylic acid and/or an ester thereof and are alike in liquid nature are mixed with each other in the same tank, no polymer precipitation occurs. The handling and storage thereof are hence easy. Consequently, tanks can be united into one, and the process is extremely advantageous in reducing the construction cost and the area necessary for equipment.