Vibrational relaxation cross sections and rate constants of HF(vϭ1) by Ar are calculated on a recent semiempirical potential energy surface ͑PES͒ ͓J. Chem. Phys. 111, 2470 ͑1999͔͒ using the quantum-mechanical coupled states approach. Accurate theoretical estimations of rate coefficients for vibrational relaxation of HF(vϭ1) at temperatures between 100 and 350 K are obtained. The vibrational relaxation is shown to be of a quasiresonant character and occur mostly to two nearest rotational levels of the ground vibrational state. The weak isotope effect after substitution of HF by DF is investigated and explained. The cross sections for vibrational relaxation of HF(v, jϭ0), where vϭ1,2,3,4, are calculated and shown to increase significantly as v increases. In the same calculations we observe a dramatic increase of multiple quantum vibrational transitions as the difference between the initial and final states falls in close resonance with the collision energy. A comparison of the cross sections obtained from the coupled states calculations with those performed with rotational infinite-order-sudden approximation proves a crucial role of molecular rotations for vibrational relaxation. Finally, we describe the close coupling coupled states calculations for relaxation and rotational excitation of HF(vϭ1, jϭ0) with a reduced number of open channels in the basis set and show that it is possible to obtain converged results for rotationally inelastic transitions between the various levels of vϭ1 neglecting all states below vϭ1, jϭ0.