There is provided a method for handling high-viscosity substances discharged from a production process of acrylic acid or esters thereof by gas-phase catalytic oxidation, which method is improved such that upon transporting the high-viscosity substances in a molten state to a storage tank through a pipeline, the retention or clogging of the high-viscosity substances in the pipeline can be effectively prevented without adding a solvent thereto, resulting in smooth transportation thereof through the pipeline. In the method for handling high-viscosity substances discharged from a production process of acrylic acid or esters thereof by gas-phase catalytic oxidation according to the present invention, when the high-viscosity substances are transported to a storage tank through a pipeline, contents of acrylic acid polymers and a polymerization inhibitor in the high-viscosity substances are controlled to not less than 40% by weight and not less than 4% by weight, respectively, and the high-viscosity substances are maintained at a temperature of not less than 110 C.