Molecular dynamics simulations are performed to study the temperature-dependent dynamics and structures of the hydration shells of elastin-like and collagen-like peptides. For both model peptides, it is consistently observed that, upon cooling, the mechanisms for water dynamics continuously change from small-step diffusive motion to large-step jump motion, the temperature dependence of water dynamics shows a weak crossover from fragile behavior to strong behavior, and the order of the hydrogen-bond network increases. The temperature of the weak crossover from fragile to strong behavior is found to coincide with the temperature at which maximum possible order of the hydrogen-bond network is reached so that the structure becomes temperature independent. In the strong regime, the temperature dependence of water translation and rotational dynamics is characterized by ail activation energy of E-a approximate to 0.43 eV, consistent with results from previous dielectric spectroscopy (DS) and nuclear magnetic resonance (NMR) studies oil protein hydration waters. At these temperatures, a distorted pi-flip motion about the 2-fold molecular symmetry axes, i.e., it water-specific beta process, is an important aspect of water dynamics, at least at the water-peptide interfaces. In addition, it is shown that the hydration waters exhibit pronounced dynamical heterogeneities, which can be traced back to a strong slowdown of water motion in the immediate vicinity of peptide molecules due to formation of water-peptide hydrogen bonds.