The effects of nonadditive forces on Ar-n-HF van der Waals clusters are investigated for n = 2, 3, 4, and 12. The pair potentials operating in these systems are accurately known. Earlier models of nonadditive forces in Ar-2-HF, including nonadditive dispersion, induction, and overlap distortion, are generalized to handle clusters of arbitrary size. Calculations of vibrational frequency shifts (redshifts) are then performed and compared with experiment. The geometries of the clusters are first optimized by simulated annealing; the Ar n cage is then held fixed, and the resulting five-dimensional Schrodinger equation is solved for the hindered rotational and translational motion of the HF molecule in the field of the Ar atoms. The nonadditive potentials are found to account remarkably well for the observed frequency shifts.