A process for preparing perylene-3,4:9,10-tetracarboxylic dianhydride, comprising: dimerizing a naphthalene-1,8-dicarboximide of the formula IIa; reoxidizing the resulting alkali metal salt of the leuco form of the perylene-3,4:9,10-tetracarboxylic diimide of the formula Ia; hydrolyzing the diimide to the tetraalkali metal salt of perylene-3,4:9,10-tetracarboxylic acid in the presence of an inert organic solvent, of an alkali metal base and of water; and subjecting the tetraalkali metal salt of perylene-3,4:9,10-tetracarboxylic acid to the action of an aqueous inorganic acid to convert it into perylene-3,4:9,10-tetracarboxylic dianhydride; wherein R3 is cyclohexyl or phenyl which may each be substituted by up to three C1-C4-alkyl radicals, and the dimerizing is in a substantially homogeneous reaction medium consisting essentially of an apolar aprotic organic solvent and an alkali metal base.