We developed a model to mimic the exciton dynamics in J-aggregates of cyanine dyes on the basis of Monte Carlo simulations. We consider the aggregates to be linear one-dimensional chains, where the in-phase combination of molecular excitons leads to a stabilization. A random distribution of segment lengths limits the effective coherence length and induces an inhomogeneous band broadening. The model takes into account the incoherent energy hopping between aggregates following the excitation. The results of the simulation could be fitted to the experimentally obtained absorption and fluorescence spectra and to the fluorescence decays of the J-aggregates of 3,3'-disulropropyl-5,5'-dichloro-thiacarbocyanine (THIATS).