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A theory of vibration-to-vibration energy transfer is developed for HF/DF(υ = 1) + HF/DF(υ = 1) → HF/DF(υ = 0) + HF/DF(υ = 2) based on the model of dimer formation. This model is shown to be primarily responsible for the energy transfer below 500 K where a strong negative temperature dependence of energy-transfer rates is found; above this temperature the rapid rotational motion of the colliding molecules causes the energy exchange to take place with the result that the rate increases with temperature in a normal fashion. The model represents the low-temperature limit of the energy-transfer process, while the rapid rotational model gives the high-temperature limiting rate, so the overall collision process can be explained in terms of these two contributions. The sum takes a minimum value near 700 K in both HF + HF and DF + DF collisions.