Band intensities for nonresonant vibrational hyper-Raman scattering depend on the derivatives of the beta hyperpolarizability, a nonlinear electronic response tenser, with respect to normal mode coordinates. In this work, we derive a new result for the change in beta(-omega(sigma);omega(1),omega(2)) due to small shifts in nuclear positions within a molecule. We prove that the derivative of beta(-omega(sigma);omega(1) omega(2)), taken with respect to the position R(K) of nucleus K, depends on the nonlocal hyperpolarizability density gamma(r,r’,r ",r;-omega(sigma)omega(1) omega(2),0) of second order, the charge on nucleus K, and the dipole propagator from R(K) to r. Thus gamma(r,r’,r ",r; -omega(sigma);omega(1) omega(2),0) determines the origins of vibrational hyper-Raman intensities on the intramolecular scale. Two observations provide the physical basis for this result : The effective value of beta for a molecule in a static applied held is governed by the gamma hyperpolarizability density. When a nucleus shifts infinitesimally, the electrons respond to the resulting change in the nuclear Coulomb field via the same nonlocal susceptibilities that characterize their response to an applied electric field.