Multiblock or multiset methods are starting to be used in chemistry and biology to study complex data sets. In chemometrics, sequential multiblock methods are popular; that is, methods that calculate one component at a time and use deflation for finding the next component. In this paper a framework is provided for sequential multiblock methods, including hierarchical PCA (HPCA; two versions), consensus PCA (CPCA; two versions) and generalized PCA (GPCA). Properties of the methods are derived and characteristics of the methods are discussed. All this is illustrated with a real five-block example from chromatography. The only methods with clear optimization criteria are GPCA and one version of CPCA. Of these, GPCA is shown to give inferior results compared with CPCA. Copyright © 2003 John Wiley & Sons, Ltd.