With many aromatic compounds in liquid solution, the population of the metastable triplet state T1 leads to delayed Sn→S0 fluorescence (DFn, n≥ 1) of the pyrene type, which results from the generation excited singlet states Sn by nonradiative triplet-triplet annihilation (TTA) T1 + T1 {rightwards squiggle arrow} Sn + S0. Knox and Swenberg have postulated that, apart from the DF1, there should be an extremely weak direct radiative TTA: T1 + T1 → S0 + S0 + hνrad. The spectrum of the direct radiative TTA is likely to be si the convolution of the phosphorescence spectrum with itself. Due to this similarity, part of the high-energy delayed luminescence from solutions of pyrene and phenazine can be assigned to direct radiative TTA. The probability of direct radiative TTA relative to the generation of Sn by nonradiative TTA is typically ≲ 5 × 10-7. With anthracene, 9-methylanthracene and 1,2-benzanthracene no similarity has been found between the spectrum of the observed high-energy luminescence and the calculated spectrum of radiative TTA. Some special aspects of the delayed fluorescence are treated: nonradiative TTA as a special case of Dexter energy transfer, the temperature dependence of the delayed excimer fluorescence from pyrene, nonequilibrium hot-band delayed fluorescence from S1 of anthracene, and the problem of the indirect determination of lifetimes of upper excited singlet states. © 1990.