The photostablities of two dozen polycyclic aromatic hydrocarbon (PAH) cations and a fullerene, C-60(+), have been tested. The molecular radical cations have been produced by both electron impact and laser desorption, then trapped and mass-analyzed in a Fourier transform ion cyclotron resonance mass spectrometer, The PAH cations were subjected to visible and UV radiation (lambda greater than or equal to 185 nm) from a Xe are lamp. Fragmentation patterns fall into four groups : photostable, hydrogen loss only, hydrogen and carbon loss, and photodestroyed. The fragmentation patterns are discussed with respect to prior experimental and theoretical models. Implications of these findings for the "PAH hypothesis" and the unidentified interstellar infrared (UIR) emission bands are discussed briefly.