Acetylenedicarboxylic acid dihydrate (ADAD) represents a complex with strong hydrogen bonding between the carboxylic OH and the water molecule. An X-ray re-examination of the ADAD crystal structure confirms the OO distance of the short hydrogen bonds, and clearly shows different bond lengths between the two oxygen atoms with respect to the carbon atom in the carboxyl group, indicating a neutral structure for the complex. The neutral structure was also confirmed by vibrational spectroscopy, as no proton transfer was observed. The diffraction studies also revealed two polymorph modifications: room temperature (α) and low temperature (β), with a phase transition at approximately 4.9 °C. The calculated vibrational spectra are in satisfactory agreement with the experimental spectra. A comparison of the structure and the vibrational spectra between the ADAD and the oxalic acid dihydrate reveals some interesting details. The crystal structures of both crystal hydrates are almost identical; only the OO distances of the strongest hydrogen bonds differ by 0.08 Å. Although it was expected that a larger OO spacing in the ADAD crystal may significantly change the infrared and Raman spectra, especially for the frequency and the shape of the acidic OH stretching vibration, both the shape and frequency are almost identical, with all subpeaks topped on the broad OH stretching vibration. The OO distance dependent are only in- and out-of-plane OH deformations modes. The presence of polarons due to the ionized defects was not observed in the vibrational spectra of ADAD. Therefore, the origin of the broad OH band shape was explained in a similar way to the acid dimers. The anharmonicity of a potential enhances the coupling of the OH stretching with the low-frequency hydrogen bond stretching, which, in addition to the Fermi resonance, structures the band shape of the OH stretching. The fine structure found as a superposition of a broad OH stretching is attributed to Davydov coupling.