There is disclosed a resist lower layer film material for a multilayer-resist film used in lithography which contains, at least, a polymer having a repeating unit represented by the following general formula (1). Thereby, there can be provided a resist lower layer film material for a multilayer-resist process, especially for a two-layer resist process, which functions as an excellent antireflection film especially for exposure with a short wavelength, namely has higher transparency, and has the optimal n value and k value, and is excellent in an etching resistance in substrate processing, and a method for forming a pattern on a substrate by lithography using it. ##STR00001##