Abstract: Surfaces of substrates, typically semiconductor device substrates, are polished with a polishing agent comprising polishing abrasive grains of a metal oxide (e.g. cerium oxide, zirconium oxide or manganese oxide) having a hydrophilic surface and a surface potential (zeta potential) of not more than 50 mV at pH 7 in absolute value, preferably polishing abrasive grains having hydrophilic groups, preferably hydroxyl groups, at the extremities and then cleaned with an aqueous cleaning solution comprising pure water. The polishing abrasive grains remaining on the polished substrate surface can be removed to a satisfactory degree therefrom by simple cleaning using the aqueous cleaning solution only.