This thesis is focused on the role that nuclear dynamics plays in the formation of X-ray absorption (XAS) and resonant inelastic X-ray scattering (RIXS) spectra of multimode free molecules. A combined approach based on ab initio electronic structure methods and quantum nuclear wave packet dynamics is applied to two systems -- water and methanol in the gas phase. An IR-pump – X-ray-probe spectroscopy of vibrationally excited water and its isotope substitutions is employed to explore different vibrational progressions of the final electronic state due to a spatial filtration of the vibrations in the core-excited state and selection rules. It was demonstrated the possibility to use RIXS as a tool to study X-ray absorption from a selected vibrational level of the ground state. IR-pump – X-ray-probe spectroscopy applied to the HDO molecule sheds light on the old classical problem of wave function collapse: we demonstrate numerically the gradual collapse of the initially localised vibrational wave function in the HDO molecule. It is also explained the dynamical nature of the splitting of the 1b₁ peak in the RIXS spectrum of H₂O, HDO and D₂O molecules. This splitting is referred to close-lying molecular and atomic-like peaks. In order to study the methanol molecule a special theoretical tool for studies of multimode molecules has been developed. This approach combines the advantages of the quantum wave packet technique for simulations of the dynamics in dissociative states with the efficiency of the Franck-Condon method for computing transitions between bound states. It is shown that the multimode nuclear dynamics plays an important role in XAS and RIXS spectra of methanol. The XAS and RIXS spectra formation was explained taking into account different dynamics in different core-excited potential energy surfaces, as well as the entanglement of vibrational modes by anharmonicity and by the life-time vibrational interference.