Phonon modes in column-III--nitride ternary semiconductors are investigated theoretically within the modified random-element isodisplacement model. It is found that ${A}_{1}$ and ${E}_{1}$ branches of optical phonons in wurtzite ${\mathrm{Ga}}_{x}{\mathrm{Al}}_{1\ensuremath{-}x}\mathrm{N}$ and ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ exhibit one-mode behavior. This result is explained by the fact that atomic mass of nitrogen is much smaller than those of other atoms.