MOTIVATED by the possibility of studying individual local environments in the solid state, there have been attempts to observe the optical absorption spectra of single impurity molecules trapped in crystals1,2. For example, time-dependent shifts in spectral features (spectral diffusion) are expected to result from motions of the molecules surrounding the impurity species. Recent advances in high-efficiency fluorescence excitation spectroscopy using ultra-thin sublimed crystals3 have now removed the earlier obstacle of low signal-to-noise ratios. Here we report the observation of jumps in the resonance frequency, on timescales of seconds to minutes, in the fluorescence excitation spectrum of single molecules of pentacene in crystals of p-terphenyl cooled to 1.5 K. These effects are seen only for some impurities, which probably correspond to pentacene molecules in particularly strained local environments; most impurities show no time-dependent behaviour. We speculate on the possible causes of these spectral jumps, although further work will be required to draw definitive conclusions about the molecular motions involved. © 1991 Nature Publishing Group.