The energy transfer between dye molecules and the mobility of the corresponding excitons are investigated in polymethyl methacrylate films highly doped with perylene bisimide dyes. The dynamics is measured by group delay corrected, femtosecond broad-band spectroscopy revealing the transfer route via absorption changes that are specific for the participating species. In films doped with 0.14 M perylene orange an ultrafast homotransfer between the dye molecules is found by analyzing the loss of the excitation-induced anisotropy. The process exhibits a stretched exponential time dependence which is characteristic for Forster energy transfer between immobilized molecules. The transfer time is 1.5 ps for an average transfer distance of 2.3 nm and results in a high mobility of the optically generated excitons. In addition, we find that the excitons move to perylene orange dimers, which have formed in low concentration during the sample preparation. The observed energy transfer time is slightly shorter than expected for a direct Forster transfer and indicates that exciton migration by multistep transfer between the monomers speeds up the transport to the dimers. In samples doped with perylene orange and perylene red heterotransfer to perylene red takes place with transfer times down to 600 fs. The mechanism is Forster transfer as demonstrated by the agreement with calculations assuming electric dipole interaction between immobilized and statistically distributed donor and acceptor units. The model predicts the correct time dependence and concentration scaling for highly doped as well as diluted samples. The results show that ultrafast exciton migration between dye molecules in highly doped matrixes is an attractive and efficient mechanism to trans port and collect energy in molecular systems and organic electronic devices. Further optimization should lead to a loss-free transport over distances typical for the thickness of active layers in these systems.