Abstract: A polishing method for a heterostructure of at least one relaxed superficial heteroepitaxial layer on a substrate made of a different material. The method includes a first chemical mechanical polishing step of the surface of the heteroepitaxial layer performed with a polishing cloth having a first compressibility ratio and with a polishing solution having a first silica particle concentration. The first chemical mechanical polishing step is followed by a second chemical mechanical polishing step of the surface of the heteroepitaxial layer, with the second step being performed with a polishing cloth having a second compressibility ratio, higher than the first compressibility ratio, and with a polishing solution having a second silica particle concentration, lower than the first concentration. By this method, improved surface roughness is achieved.