In this chapter, the authors discusses the collective excitations for a one-dimensional chain with a charge density wave ground state and derive the dispersion relation of the excitations in terms of the parameters of the Ginzburg-Landau theory. The excitations of the spin density wave ground state are more complex, as both charge and spin degrees of freedom are important. At zero temperature, with no screening by quasiparticles, the long range Coulomb interactions become important, and this leads to a gap in the phason spectrum for longitudinal excitations as first pointed out by Anderson and Higgs. The excitations of the amplitude and phase also contribute to the various thermodynamic quantities. With both spin and charge degrees of freedom available, various types of amplitude and phase excitations may occur. Spin orbit and dipole-dipole interactions remove the rotational symmetry of the magnetic excitations and lead to an energy gap in the spin wave excitation spectrum.