A calculation is presented of the radiative lifetimes of theππ′phosphorescent state of quinoxaline and a number of aromatic hydrocarbons. For the matrix elements of the spin-orbit hamiltonian an ‘atoms in molecules’ approach is used and only the one-electron one-centre terms in the expansion of these matrix elements in integrals over AO's are retained. This approach is similar to that used by Goodman and Krishna for thenπ′states of some aza-aromatics. For quinoxaline a lifetimeτ=0·33 s is obtained.