For an electron-phonon system with several equivalent bands a closed set of integral equations is solved self-consistently using real-time Green's functions. A multiple-band Peierls-Boltzmann equation is deduced from the Bethe-Salpeter equation for the electron density. Relaxation-time approximation together with local particle number conservation allows the calculation of the dielectric response and the displacement response generalized for the multiple-band case. The poles of the latter response function, essentially governed by electron density fluctuations, determine three coupled modes. A soft-mode instability is found in agreement with A15- compounds.
