By the spin-allowed annihilation of two metastable triplet states (triplet-triplet annihilation-TTA) one electronic ground state (S0) and one electronically excited singlet (Si) or triplet (Ti) or quintet (Qk) state are created, provided the sum of the excitation energies of the two metastable triplet states is sufficient for the creation of the particular excited state. On the basis of semi-empirical calcns. of the excitation energies of T1 and Q1 of forty-six conjugated org. compds. it is shown that Q1 of benzene and some other compds. should be accessible through annihilation of like triplets (homo-TTA), and that Q1 of many compds. should be accessible through annihilation of unlike triplets (hetero-TTA). The population of Q1, competing with that of S1, should cause an unusual magnetic-field dependence of the delayed fluorescence S1 -> S0. In favorable cases, the population of Q1 should lead to an inverse (pos.) magnetic high-field effect on the delayed fluorescence.