Subject classification: 74.25.Kc We discuss the phonon self-energy in the presence of isotropic and anisotropic gaps, which originate from the charge (CDW) and spin-density waves (SDW). In order to connect our results to the problem of high-temperature superconductivity a two-dimensional lattice has been considered. The shift of the phonon frequency and the modification of the linewidth is investigated for different phonon momenta. We show that the onset of a gap leads predominantly to the hardening of low frequency modes and softening of modes, which correspond to higher frequencies. In the latter case the modification of phonon properties depends on the symmetry of the gap. For the isotropic gap the softening of frequencies is important only for phonons with small momentum, whereas for the d-wave gap also properties of phonons with large momentum can seriously be modified.

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