The rapidity and high degree of molecular vibrational excitation by the absorption of ir laser light in SF₆ and other molecules may be due in large part to the anharmonic splitting of excited vibrational states. Anharmonic splitting of an overtone or combination vibrational level (i) is possible only in molecules with degenerate vibrational states, (ii) can be comparable in magnitude to the net anharmonic shift of the level, (iii) is generally much larger than the rotational shifts which have previously been proposed as an explanation for the dissociation of SF₆. We find that consecutive nearly resonant transitions are possible in SF₆ up to υ₃ = 5 to 10.