The formation of amyloid fibrils of α-synuclein (αSyn), the key protein in Parkinsons disease, is an autocatalytic process that is seeded by mature αSyn fibrils. Based on systematic measurements of the dependence of the fibril growth rate on the concentrations of monomers and preformed fibrillar seeds, we propose a mechanism of αSyn aggregation that includes monomer binding to fibril ends and secondary nucleation by fibril breaking. The model explains the increase of the αSyn aggregation rate under shaking conditions and the exponential increase in the fraction of fibrillar protein at the initial stages of αSyn aggregation. The proposed autocatalytic mechanism also accounts for the high variability in the aggregation lag time. The rate constant of monomer binding to the ends of fibrils, k+ ∼1.3 mM-1 s-1, was estimated from the aggregation rate and previously reported average fibril lengths. From the aggregation rates at low concentrations the binding of monomeric αSyn to fibrils was found to be almost irreversible, with an equilibrium dissociation constant (Kd) smaller than 3 μM.