Molecular crystals produce hyper-Rayleigh scattering (HRS) at the second harmonic frequency via nonzero mean-square dynamical fluctuations in the quadratic optical susceptibility. The intensity of HRS depends on the lattice normal-coordinate derivatives of the quadratic susceptibility. Expressions are derived for these quantities, including polarizability changes induced by polar molecules and the first hyperpolarizability induced by quadrupolar molecules, drawing upon previous results from microscopic theories of nonlinear optics, Raman scattering, and optical activity. A simple illustrative calculation for the hexamine crystal indicates that its HRS should be governed by a susceptibility that is about 7% of the usual quadratic susceptibility for second-harmonic generation (SHG). HRS should be detectable for a centrosymmetric crystal where SHG is zero by symmetry. (C) 2001 American Institute of Physics.