α-synuclein (αSyn) is a protein consisting of 140 amino acid residues and is abundant in the presynaptic nerve terminals in the brain. Although its precise function is unknown, the filamentous aggregates (amyloid fibrils) of αSyn have been shown to be involved in the pathogenesis of Parkinson's disease, which is a progressive neurodegenerative disorder. To understand the pathogenesis mechanism of this disease, the mechanism of the amyloid fibril formation of αSyn must be elucidated. Purified αSyn from bacterial expression is monomeric but intrinsically disordered in solution and forms amyloid fibrils under various conditions. As a first step toward elucidating the mechanism of the fibril formation of αSyn, we investigated dynamical behavior of the purified αSyn in the monomeric state and the fibril state using quasielastic neutron scattering (QENS). We prepared the solution sample of 9.5 mg/ml purified αSyn, and that of 46 mg/ml αSyn in the fibril state, both at pD 7.4 in D2O. The QENS experiments on these samples were performed using the near-backscattering spectrometer, BL02 (DNA), at the Materials and Life Science Facility at the Japan Accelerator Research Complex, Japan. Analysis of the QENS spectra obtained shows that diffusive global motions are observed in the monomeric state but largely suppressed in the fibril state. However, the amplitude of the side chain motion is shown to be larger in the fibril state than in the monomeric state. This implies that significant solvent space exists within the fibrils, which is attributed to the αSyn molecules within the fibrils having a distribution of conformations. The larger amplitude of the side chain motion in the fibril state than in the monomeric state implies that the fibril state is entropically favorable.