We present results of a comparative study of the vibrational spectrum and local density of phonon states in ordered p(2 x 2) and (√3 x √3)R30° structures formed by potassium atoms on the Pt(111) surface. The calculations were performed with tight-binding interatomic interaction potentials. It was found that the mode associated with vertical displacements of K adatoms has an energy of about 20 meV in both K structures. The strength and energy of this mode slightly decreases with increasing coverage. This result is in good agreement with available experimental data. As in time-resolved second harmonic generation measurements, we observed low frequency modes for both structures considered, which are caused by the interaction of potassium with the second layer of the substrate.