Part of the lattice vibrational (phonon) spectra of the compounds Ce2Mg3(N03) .24H20 and La2Mg (NO3)12'24H2° have been investigated by means of Raman spectroscopy. After a short discussion of the mechanism of inelastic scattering of light (Raman spectroscopy), the theory of lattice vibrations and the activity of the phonons is presented. The complete selection rules for the crystals are obtained by carrying out a factor group analysis together with a detailed discussion of the crystallographic structure of the double nitrate salts. Comparison of the Raman spectra of the Lanthanum and Cerium double nitrates indicates that both have the same structure. The existence of hydrogen bonding among the oxygen atoms of the N0~ groups and hydrogen atoms of water molecules is shown from the observed shift of the NO modes with temperature, and also, the shift of the normal modes of the water molecules.