Results of application of pseudospectral methods, also known as spectral collocation methods, to practical particulate processes including growth, nucleation, aggregation, and breakage are presented. For growth-dominated processes, a considerable reduction in model dimension can be achieved; for pure aggregation and breakage they form a viable option. To handle problems that include aggregation, breakage, and growth phenomena simultaneously, we introduce a hybrid algorithm combining the advantages of spectral methods and cell average or fixed pivot methods for aggregation and breakage. Results are shown for analytical examples as well as real processes taken from the fields of granulation and crystallization. (C) 2011 American Institute of Chemical Engineers AIChE J, 58: 23092319, 2012