Femtosecond pump–probe spectroscopy is applied to thin films of the quasi-one-dimensional organic semiconductor 3,4,9,10-perylene tetracarboxylic dianhydride (PTCDA). We present transient absorption spectra over a broad spectral range. Ultrafast intraband relaxation in the S 1 manifold towards the border of the Brillouin zone is shown to depend on temperature and excitation density. The intraband relaxation time is of the order of 100fs. At high excitation densities (>10 19 cm −3 ), the major de-excitation mechanism for the relaxed excitons is exciton–exciton annihilation. The experimental decay dynamics can be explained very well by two alternative annihilation models: one-dimensional diffusion limited bimolecular recombination or single-step long range Förster-type annihilation. In contrast, a three-dimensional diffusion limited annihilation model is significantly inferior. For all three models, we extract annihilation rates, diffusion constants, diffusion lengths, and Förster radii for room and liquid Helium temperature.