The sequences of Fermi resonances ν_s ≈ 2ν_b in the IR spectrum of a fluoroform solution (CHF₃) in liquefied krypton have been studied. Here, ν_s is the CH-stretching vibration and ν_b is the bending vibration. It has been shown that it is necessary to use an extended set of spectroscopic parameters for the correct description of resonant multiplets at a high degree of vibrational excitation. Among other factors, it is necessary to consider the dependence of the anharmonic interaction constant α_sbb on the vibrational quantum numbers. The conclusions are generalized for the arbitrary case of the CH-chromophore CHX₃.