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