[en] Heat-capacity (2--400 K) and inelastic-neutron-scattering studies of the phonon spectra are reported for superconducting, high-critical-field, Chevrel-phase, lead and tin molybdenum sulfides (T/sub c/approx.11--15 K). Nine phonon modes per unit cell are identified whose frequencies are in the immediate region Bergmann and Rainer indicate is necessary to optimize T/sub c/. Acoustic-phonon softening on cooling is observed. A molecular-crystal model is proposed for the lattice dynamics of these materials