We report the results of a theoretical study of fluorescence dynamics in quasi-one-dimensional systems with phonon-assisted energy transfer between nearest neighbors. It is assumed that the phonons are three-dimensional, the one-phonon mechanism is dominant and the wavelength of the phonon involved is long in comparison with the separation between nearest neighbors. A combination of analytical and numerical techniques is used in the analysis of the decay of the narrow-line component observed in fluorescence line narrowing studies. A random distribution of single-ion transition frequencies is postulated, with no correlation between sites, and the variance of the distribution is taken to be small in comparison with (kT/(h) over bar)(2). It is found that the narrow-line fluorescence decays asymptotically as t(-1/3) rather than as t(-1/2). as would be the case if the energy transfer were diffusive at long times. It is shown that the subdiffusive dynamics reflects a singular behavior in the limiting form of the distribution of transfer rates that is not present when the energy transfer involves two-phonon processes. Numerical results are presented for the early stages of the decay for rectangular distributions of transition frequencies with various values of the ratio of kT/(h) over bar sigma, where sigma(2) is the variance of the distribution. (C) 1999 Elsevier Science B.V. All rights reserved.