The ultrafast dissipative exciton motion in a molecular dimer of the light harvesting complex II of higher plants is investigated theoretically. The density matrix formalism is applied to simulate the one- and two-color pump-probe spectra measured by Bittner ct al.(1) To incorporate coherent vibrational motion we use a representation in localized exciton vibrational states. The observed ultrafast transfer dynamics on the subpicosecond time scale can be well explained by means of a delocalization of the exciton wave function over both monomers. For the low-temperature one-color pump-probe measurement we predict quantum beats in the signal due to coherent nuclear wave packet motion. Furthermore, our calculations support the in-line geometry for the Chlorophyll a/b dimers in the pigment-protein complex.