Quasiclassical trajectories were used to study the energy transfer rates and mechanisms in collisions of HF(v,J) with CO. A potential-energy surface was formulated by using spectroscopic and ab initio information. We have computed state-to-state rates for HF (v(i) = 3,5,7,9; J(i) = 2) + CO(v(i) = 0) --> HF(v(f),J(f)) + CO for a thermal distribution of translational energies and CO rotational states at 300 K. The relaxation is due predominantly to vibration-to-rotation energy transfer with DELTAv= -1. As the initial vibrational state is increased, multiquantum transitions (DELTAv < -2) become increasingly important. The computed results are in good agreement with experimental results.