The results of theoretical and experimental research of the problem of revealing hidden images on paintings in the infra-red are discussed. Experimental estimates of the spectral absorbance of paints have resulted in defining the intervals of IR-region where the paints may be considered as pure scattering systems. Thus a theory has been built which satisfactorily explains the main experimental resultsobserved in IR-reflectography of paintings. The theory seems to suit the purpose better than the application of the Kubelka-Munk approximation used in van Asperen de Boer's works of 1968-1974. Some types of IR-reflectographical systems commonly used for studying paintings are examined critically. Some new lines of the development of IR-reflectographical equipment are described.