Analytical expressions are derived for the incoherent and coherent dynamic structure factor of macromolecules in a melt. In particular, the influence of chain stiffness on these quantities is investigated. For scattering vectors qpi p/2 the incoherent dynamic structure factor is shown to be a universal function of only the combination q(8/3)tp(1/3), reflecting the strong influence of the local chain stiffness on dynamical properties at small length scales. Moreover, the q dependence of both the full width at half maximum of the Fourier transformed incoherent dynamic structure factor and the initial decay rate of the coherent dynamic structure factor are calculated. The comparison of the theoretical results with quasielastic neutron scattering experiments of different polymers exhibits good agreement.