Formation of amyloids is the hallmark of several neurodegenerative pathologies. Structural investigation of these complex transformation processes poses significant experimental challenges due to the co-existence of multiple species. The additive nature of small-angle X-ray scattering (SAXS) data allows for probing the evolution of these mixtures of oligomeric states, but the decomposition of SAXS data into species-specific spectra and relative concentrations is burdened by ambiguity. We present an objective SAXS data decomposition method by adapting the multivariate curve resolution alternating least squares (MCR-ALS) chemometric method. The approach enables rigorous and robust decomposition of synchrotron SAXS data by simultaneously introducing these data in different representations that emphasize molecular changes at different time and structural resolution ranges. The approach has allowed the study of fibrillogenic forms of insulin and the familial mutant E46K of α-synuclein, and is generally applicable to any macromolecular mixture that can be probed by SAXS.