Amyloid fibril formation is a hallmark of neurodegenerative disease caused by protein aggregation. Oligomeric protein states that arise during the process of fibril formation often coexist with mature fibrils and are known to cause cell death in disease model systems. Progress in this field depends critically on development of analytical methods that can provide information about the mechanisms and species involved in oligomerization and fibril formation. Here, we demonstrate how the powerful combination of diffusion NMR and multilinear data analysis can efficiently disentangle the number of involved species, their kinetic rates of formation or disappearance, spectral contributions, and diffusion coefficients, even without prior knowledge of the time evolution of the process or chemical shift assignments of the various species. Using this method we identify oligomeric species that form transiently during aggregation of human superoxide dismutase 1 (SOD1), which is known to form misfolded aggregates in patients with amyotrophic lateral sclerosis. Specifically, over a time course of 42 days, during which SOD1 fibrils form, we detect the disappearance of the native monomeric species, formation of a partially unfolded intermediate in the dimer to tetramer size range, subsequent formation of a distinct similarly sized species that dominates the final spectrum detected by solution NMR, and concomitant appearance of small peptide fragments.