We calculate the dynamic structure factor S(k, ω) of liquid Ge (ℓ-Ge) at temperature T = 1250 K, and of amorphous Ge (a-Ge) at T = 300 K, using ab initio molecular dynamics. The electronic energy is computed using density-functional theory, primarily in the generalized gradient approximation, together with a plane wave representation of the wave functions and ultra-soft pseudopotentials. We use a 64-atom cell with periodic boundary conditions, and calculate averages over runs of up to about 16 ps. The calculated liquid S(k, ω) agrees qualitatively with that obtained by Hosokawa et al, using inelastic X-ray scattering. In a-Ge, we find that the calculated S(k, ω) is in qualitative agreement with that obtained experimentally by Ma- * Present address: