A method is provided for preventing an easily polymerizable substance from being polymerized in a thin-film type evaporating device by supplying a solution of the substance to the evaporating heating surface of the device by the centrifugal force of a stirring rotary shaft, characterized by mixing a distilled vapor of the substance with a molecular oxygen-containing gas and supplying the extracted liquid or a solution having lower viscosity than the extracted liquid to a feed raw material inlet thereby adjusting the quantity of a wetting liquid per unit length of the surface in the range of 0.02-2 m3/mHr. In the evaporation of the substance by the use of the device, a method for preventing the substance from polymerization is provided.