Inelastic neutron scattering spectra of DNA-fibers are analyzed using ideas formulated recently in the field of the glass transition. The analysis reveals two temperatures, namely, T similar to 180-200 K and T similar to 230 K, at which the dynamics of DNA exhibits qualitative changes. The former is similar to the glass transition temperature, whereas the latter is similar to the crossover temperature recognized now as an important point for the dynamics of the glass transition. Exactly in this temperature range many other hydrated biopolymers show some dynamic transition and strong slowing down of their functions. The crossover temperature appears to be close to the crossover temperature of bulk water. A possible relation of the dynamic transition to functions of biomolecules and also to the dynamic transition in the hydration shell is discussed.