Nonadditive, three-body dipoles are detected experimentally in far-infrared absorption by inert gas mixtures and in triple transitions, the absorption of a single photon by three molecules, each of which becomes vibrationally excited. In this work, we use perturbation theory to derive the nonadditive, three-body dipole of molecules A, B, and C of arbitrary symmetry, interacting at long range. Our results include linear induction, hyperpolarization, dispersion, and concerted induction-dispersion effects, with direct overlap damping. We derive exact, new equations for the dispersion and induction-dispersion dipoles, in terms of the polarizabilities and hyperpolarizabilities of A, B, and C, integrated over imaginary frequencies. With these, we obtain accurate numerical results for the dipoles of inert gas trimers and trimers containing H-2, isotropically averaged over the orientations of the molecular axis. For application to heavier systems, we develop a new constant-ratio approximation, relating three-body dipoles to the van der Waals interaction energy coefficients C-6 and C-9, the static polarizability alpha, and the static dipole(2)-quadrupole hyperpolarizability B. For the test cases in this work, this approximation gives the integrals appearing in the induction-dispersion dipoles with root-mean-square errors of 10-14%, and the integrals in the pure dispersion dipoles with root-mean-square errors of 1-4%. Our numerical results for the dipoles of inert gas trimers should be useful in molecular dynamics simulations of far-infrared absorption, and in extracting information on intercollisional interference from the absorption line shapes. (C) 1997 American Institute of Physics.