The intramolecular nuclear wave packet dynamics of carboxy-deuterated o-phthalic acid monomethylester following ultrafast excitation of the OD stretching vibration in the, hydrogen bond is investigated. On the basis of quantum chemical calculations of the normal modes as well as the anharmonicities, a three-dimensional model is proposed comprising the OD stretching and bending as well as a low-frequency mode which modulates the hydrogen bond geometry. The interaction with the remaining intramolecular and solvent degrees of freedom is incorporated within a quantum master equation formulation. The linear absorption spectrum is shown to be dominated by a Fermi resonance, with the actual line widths depending on pure dephasing as well as on a fourth-order relaxation process. The latter involves two intramolecular vibrational quanta plus a solvent phonon. It proves to be vital for the explanation of the very fast relaxation of the fundamental OD stretching excitation. Further, it is shown that in the OD ground state vibrational coherences with respect to the low-frequency mode are completely dephased only after about 2 ps. These results are discussed in the context of recent infrared pump-probe and four-wave-mixing experiments.