Perylene-3,4:9,10-tetracarboxylic acid imide compounds of formula (I), including its optical antipodes and their mixtures, particularly their racemates, are new. A1 = a group of formula (i); A2 = a group of formula (ii); R1-R14 = H or optionally substituted carbocyclic aromatic group, optionally substituted heterocyclic aromatic group, halo, optionally substituted 1-18C alkyl, OR15, CN, NR16R17, COR18, NR19COR18, NR15COOR18, NR15CONR16R17, NHSO2R18, SO2R18, SOR11, SO2OR18, CONR16R17, SO2NR16R17, N=NR20, OCOR18 or OCONHR18, where pairs of adjacent groups optionally form a carbocyclic or heterocyclic ring; R18 = 1-18C alkyl, 6-10C aryl, benzyl (optionally substituted by halo, 1-4C alkyl or 1-4C alkoxy), or 5- to 7-membered heterocyclyl; R16, R17 = H or 1-18C alkyl, 3-24C cycloalkyl, 6-10C aryl or 5- to 7-membered heteroaryl (all optionally substituted by CN or OH) or R16 and R17, together with 1 of R1-R14 = 5- or 6-membered carbocyclyl or heterocyclyl; R15 = H, 1-18C alkyl, 3-24C cycloalkyl, 6-10C aryl or 5- to 7-membered heteroaryl; R19 = H or 1-18C alkyl, 3-24C cycloalkyl or 1-4C alkylaryl (all optionally substituted by CN, OH or 1-4C alkoxycarbonyl), 6-10C aryl (optionally substituted by halo, 1-4C alkyl or 1-4C alkoxy) or 5- to 7-membered heterocyclyl and R20 = a coupling component or 6-10C aryl (optionally substituted by halo, 1-4C alkyl or 1-4C alkoxy).    USE -   (I) are useful as colourants (a) for mass colouring polymers; (b) as vat dyes or mordent dyes; (c) for the preparation of paints, paint systems, particularly automotive lacquers, coating compositions, paper colours, printing inks, inks, particular for use in ink-jet printers, preferably in homogeneous solution as fluorescent ink, and for painting and writing applications and in electrophotography, e.g. for dry copier systems and laser printers; (d) for security marking applications; (e) as an additive to colourants, such as pigments and dyes, where a specific colour shade is to be achieved; (f) for marking objects for machine recognition via fluorescence; (g) for converting the frequency of light; (h) for production of passive display elements for display, notice and marking applications; (i) as starting material for supraconducting organic materials; (j) for marking with fluorescence in the solid state; (k) for decorative and artistic applications; (l) for tracer applications; (m) as fluorescent dyes in highly sensitive detection processes; (n) as dyes or fluorescent dyes in optical light collection systems, in fluorescence solar collectors, in fluorescence-activated displays, in cold light sources used for light-induced polymerisation for the preparation of plastics, for testing of materials, in photoconductors, in photographic processes, in display, illumination or image converter systems, as part of a semiconductor circuit, in chemiluminescent systems, in luminescence immunoassays or other luminescence detection processes, as signal points, in dye lasers, in optical recording media, in colour filters and (o) as rheology improvers.    ADVANTAGE -   (I) are highly fluorescent and their fluorescence is shifted towards the long wave as compared to the corresponding starting compounds. The UV/Vis spectra of compounds (I) can be influenced by substituents without adversely affecting product properties such as photostability. (I) are soluble.