The phosphorescence spectra of triphenylene and truxene, recorded in glassy solvents at 77 K, are presented. Their vibronic structure is interpreted on the basis of intensities computed with the help of quantum-chemical calculations. It is shown to be due to Herzberg-Teller-active nontotally symmetric modes which provide false origins for progressions of totally symmetric modes. Similarly to benzene, the dominant contribution to the T-1 --> S-0 transition in the two disklike molecules is shown to derive from triplet-triplet transition dipole moments. Radiative triplet lifetimes are estimated on the basis of computed oscillator strengths and compared with the correspondingly observed values.