Novel perylene compounds based on perylene-3,4,9,10-tetracarboxylic acid monoanhydride monoimides which are substituted by alkylene- or arylenesulfonic acid groups on one or both imide nitrogen atoms, or on corresponding tetracarboxylic acid diimides, or on a halogenation product thereof, have properties which render them accessible, in addition to their use as dispersing agent for pigments of the same class of compound or other categories, also for direct use as pigments and fluorescent dyestuffs as well as polymer-soluble dyestuffs.