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The second-order Raman spectrum of NaF has been measured using an argon laser source. For a light beam incident along the  direction, polarized along the  direction, and viewed along the  direction, the scattered radiation is almost completely polarized. It is shown theoretically that it is possible to account for the polarization and the detailed shape of the observed spectrum within the experimental resolution using a Raman polarizability tensor whose second derivatives with respect to nuclear displacements depend only on the positions of first neighbors in the crystal, provided one uses the phonon frequencies derived from a deformation dipole model that includes second-neighbor F--F- interactions. By assuming that the polarizability is affected only by central displacements of the nearest neighbors, the number of independent polarizability derivatives is reduced from eight to three. This assumption also gives a vanishing depolarized intensity in agreement with the experimental results. The second-order difference spectra have also been evaluated, and are found to be much more sensitive to the relative magnitudes of the various polarizability derivatives.