Photon correlation spectroscopy is used to study the internal dynamics of self-assembled charged peptide fibrils. Short neutral and charged polymeric aggregates have diffusive modes due to whole macromolecular motion. For long semiflexible fibrils the logarithm of the intermediate scattering function follows a q(2)t(3/4) scaling at long times consistent with a Kratky-Porod free energy and preaveraged Oseen hydrodynamics. Persistence lengths on the order of micrometers are calculated for the peptide fibrils consistent with estimates from the liquid-crystalline phase behavior. Fibril diameters (5-35 nm) calculated from the initial decay of the correlation functions are in agreement with transmission electron microscopy measurements.