Energy-gap-dependent vibrational-energy transfers among the nitrile stretches of KSCN/(KSCN)-C-13/(KSCN)-C-13-N-15 in D2O, DMF, and formamide liquid solutions at room temperature were measured by the vibrational-energy-exchange method. The energy transfers are slower with a larger energy donor/acceptor gap, independent of the calculated instantaneous normal mode (phonons in liquids) densities or the terahertz absorption spectra. The energy-gap dependences of the nonresonant energy transfers cannot be described by phonon compensation mechanisms with the assumption that phonons are the instantaneous normal modes of the liquids. Instead, the experimental energy-gap dependences can be quantitatively reproduced by the dephasing mechanism. A simple theoretical derivation shows that the fast molecular motions in liquids randomize the modulations on the energy donor and acceptor by phonons and diminish the phonon compensation efficiency on energy transfer. Estimations based on the theoretical derivations suggest that, for most nonresonant intermolecular vibrational-energy transfers in liquids with energy gaps smaller than the thermal energy, the dephasing mechanism dominates the energy-transfer process.