Self-assembly of misfolded proteins into ordered fibrillar aggregates known as amyloid results in numerous human diseases. Despite an increasing number of proteins and peptide fragments being recognised as amyloidogenic, how these amyloid aggregates assemble remains unclear. In particular, the identity of the nucleating species, an ephemeral entity that defines the rate of fibril formation, remains a key outstanding question. Here, we propose a new strategy for analyzing the self-assembly of amyloid fibrils involving global analysis of a large number of reaction progress curves and the subsequent systematic testing and ranking of a large number of possible assembly mechanisms. Using this approach, we have characterized the mechanism of the nucleation-dependent formation of beta(2)-microglobulin (beta(2)m) amyloid fibrils. We show, by defining nucleation in the context of both structural and thermodynamic aspects, that a model involving a structural nucleus size approximately the size of a hexamer is consistent with the relatively small concentration dependence of the rate of fibril formation, contrary to expectations based on simpler theories of nucleated assembly. We also demonstrate that fibril fragmentation is the dominant secondary process that produces higher apparent cooperatively in fibril formation than predicted by nucleated assembly theories alone. The model developed is able to explain and predict the behavior of beta(2)m fibril formation and provides a rationale for explaining generic properties observed in other amyloid systems, such as fibril growth acceleration and pathway shifts under agitation.