For atoms or molecules of D-infinity h or higher symmetry, this work gives equations for the long-range, collision-induced changes in the first (Delta beta) and second (Delta gamma) hyperpolarizabilities, complete to order R(-7) in the intermolecular separation R for Delta beta, and order R(-6) for Delta gamma. The results include nonlinear dipole-induced-dipole (DID) interactions, higher multipole induction, induction due to the nonuniformity of the local fields, back induction, and dispersion. For pairs containing H or He, we have used ab initio values of the static (hyper)polarizabilities to obtain numerical results for the induction terms in Delta beta and Delta gamma. For dispersion effects, we have derived analytic results in the form of integrals of the dynamic (hyper)polarizabilities over imaginary frequencies, and we have evaluated these numerically for the pairs H ... H, H ... He, and He ... He using the values of the fourth dipole hyperpolarizability epsilon(-i omega; i omega, 0, 0, 0, 0) obtained in this work, along with other hyperpolarizabilities calculated previously by Bishop and Pipin. For later numerical applications to molecular pairs, we have developed constant ratio approximations (CRA1 and CRA2) to estimate the dispersion effects in terms of static (hyper)polarizabilities and van der Waals energy or polarizability coefficients. Tests of the approximations against accurate results for the pairs H ... H, H ... He, and He ... He show that the root mean square (rms) error in CRA1 is similar to 20%-25% for Delta beta and Delta gamma for CRA2 the error in Delta beta is similar, but the rms error in Delta gamma is less than 4%.