The dynamics and mobility of excitons in J-aggregates of perylene bisimides are investigated by transient absorption spectroscopy with a time resolution of 50 fs. The transient spectra are compatible with an exciton delocalization length of two monomers and indicate that vibrational and configurational relaxation processes are not relevant for the spectroscopic properties of the aggregates. Increasing the pump pulse energy and in that way the initial exciton density results in an accelerated signal decay and pronounced exciton exciton annihilation dynamics.. Modeling the data by assuming a diffusive exciton motion reveals that the excitons cannot migrate freely in all three directions of space but their mobility is restricted to one dimension. The observed anisotropy supports this picture and points against direct Forster-transfer-mediated annihilation between the excitons. A diffusion constant of 1.29 nm(2)/ps is deduced from the fitting procedure that corresponds to a maximal exciton diffusion length of 96 nm for the measured exciton lifetime of 3.6 ns. The findings indicate that J-aggregates of perylene bisimides are promising building blocks to facilitate directed energy transport in optoelectronic organic devices or artificial light-harvesting systems.