Four intermolecular vibrational states of the weakly bound complexes Ar2HF and Ar2DF have been studied via high-resolution infrared spectroscopy. The vibrations are accessed as combination bands built on the v = 1 HF or DF intermolecular stretch. These van der Waals vibrational states correlate adiabatically with j = 1 motion of a hindered HF/DF rotor, corresponding to librational motion either in, or out of, the molecular plane. The vibrational origins of the Ar2HF in-plane and out-of-plane bends are 4008.9665(24) and 4035.174 41(86) cm(-1), respectively, which are 62.374 and 88.582 cm(-1) above the origin of the intermolecular ground state in the v(HF) = 1 manifold. For Ar2DF, the in-place and out-of-plane origins are 2939.836 63(4) and 2967.101 29(5) cm(-1), respectively, which correspond to intermolecular bending frequencies in the v(DF) = 1 manifold 44.852 and 72.117 cm(-1). Two dimensional angular calculations are presented which solve for the hindered rotor HF/DF eigenfunctions and eigenvalues on a pairwise additive potential constructed using a rigid Ar-2 framework; the predicted bending frequencies reproduce the correct energy ordering of the vibrational levels, but are systemically greater than experimentally observed. Rigorous full five-dimensional theoretical calculations of the intermolecular vibrational frequencies by Ernesti and Hutson [Phys. Rev. A 51 239 (1995)] in the full pairwise additive surface are found to be as much as 11% higher than the experimental values, indicating the presence of three-body repulsive contributions to the true angular potential. Inclusion of conventional three-body dispersion and induction terms can only account for a minority (approximate to 1/3) of the observed discrepancies. The majority (approximate to 2/3) of the vibrational shifts can be attributed to three-body "exchange" effects, i.e., the strongly anisotropic interaction of the HF/DF dipole with an exchange quadrupole formed by Ar-Ar. Inclusion of all three nonadditive terms (dispersion, induction, and exchange) improves the agreement with experiment by up to an order of magnitude.