The stimulated Raman scattering (SRS) was found to be an attractive way to shift laser radiation frequency to the desired spectral region. For a constant pump field with intensity Ip the Stokes field grows exponentially: Is(l) = Is(0) exp{gss Ip l}, where gss is the Raman gain coefficient and l is the length of the Raman medium. In terms of spontaneous Raman scattering cross-section the steady state Raman gain coefficient gss can be written as:formulawhere λ p and λ s are the pump and the Stokes wavelengths, N is the density of scattering centers, dσ/dΩ, is a spontaneous Raman scattering cross-section and ΔωR is the full-width at half maximum (FWHM) of the SRSactive Raman line [1]. The Raman gain coefficient is inversely proportional to the linewidth of the Raman transition ΔωR, which is a fundamental property of a certain material. It is determined by the relaxation paths due to the phonon-phonon coupling. High frequency Raman vibrations in molecular ionic crystals are originated inside molecular ion (internal vibrations) and are well isolated from lattice phonons (external vibrations). That's why the number of their possible relaxation channels is limited and they can be easily interpreted in terms of multiphonon decay mechanisms. Previously there was a number of publications on the vibration relaxation of internal modes in some molecular ionic crystals. The obtained results for different molecular ionic crystals have shown that the temperature dependence of the line broadening provided fundamental information on the dominant mechanism leading to vibrational relaxation. The theory of the relaxation processes in molecular crystals showed that the full bandwidth γ i for an internal vibron ω i in an ideal crystal equals to the sum of several contributions, each arising from a specific depopulation or dephasing mechanism [2]. The analysis of temperature broadening of SRS-active Ag(ν1) mode in tungstate and molybdate sheelite crystals showed that the vibronic relaxation with high accuracy could be described as a combination of two processes [3]. At low temperature the relaxation goes mostly in the two-phonon splitting path with the excitation of a lower energy mode and lattice phonon. At higher temperature the dominant is a dephasing process due to the interaction of the Ag(ν1) internal vibron with highly populated low energy lattice phonons. The probability of two-phonon splitting process at low temperature is higher than that for three-phonon splitting process. This results in the shorter lifetime of vibronic excitation for Ag(ν1) mode and broader linewidth, In Ref. [3] the linewidths of Ag(ν1) SRS-active mode in CaMoO4 and PbMoO4 crystals are shown to be 5.6 cm-1 and 6 cm-1 correspondingly. It is in contrary with the vibronic relaxation in Ba(NO3)2 crystal [4] in which the absence of two-phonon splitting relaxation process for Ag(ν1) mode results in longer vibronic lifetime and narrow mode linewidth (ΔωR = 0.4 cm-1). The relaxation mechanisms were determined in the range of sheelite tungstates and molybdates with Ca, Sr, Ba and Pb cations which corresponds to the relative shift of Raman modes frequencies in these crystals. Narrower Ag(ν1) SRS-active Raman modes among sheelites were observed in barium tungstate (ΔωR = 1.6 cm-1). and barium molybdate (ΔωR = 1.9 cm-1) which well correlates with the peculiarities of sheelite crystal structure.