A coupled states quantum scattering study of vibrational relaxation in Ar + HF and Ar + HCl collisions is presented. The energy transfer in these systems exhibits a quasiresonant character resulting in a strongly inverted rotational population of the diatomic molecules after collision. The high anisotropy of interaction is shown to be determining the quasiresonant vibrational energy transfer by favoring the population of high rotational energy levels. The role of interaction anisotropy in atom-diatomic molecule collisions is discussed.