The work deals with the establishment of the dependence of the vibrational frequencies of strong O–H⋯O and N–H⋯O hydrogen bonds for the diagnosing the bonds themselves. To this end, the Raman spectra of a large number of different normal and deutero-substituted crystals characterized by the presence of strong O–H⋯O and N–H⋯O bonds are measured and the quantum chemical calculation is performed for one of these compounds. The dependence of the O–H stretching frequency on the O⋯O distance is constructed differing from that previously known for short O⋯O contacts. The mechanisms of significant broadening of the O–H vibration band in strong O–H⋯O hydrogen bonds are considered. Different dependences of the N–H vibrational frequencies in N–H⋯O bonds are reported and the causes of this diversity are discussed.