Multiway principal component analysis (MPCA) and multiway partial-least squares (MPLS) are well-established methods for the analysis of historical data from batch processes, and for monitoring the progress of new batches. Direct measurements made on prior batches can also be incorporated into the analysis by monitoring with multiblock methods. An extension of the multiblock MPCA/MPLS approach is introduced to explicitly incorporate batch-to-batch trajectory information summarized by the scores of previous batches, while keeping all the advantages and monitoring statistics of the traditional MPCA/MPLS. However, it is shown that the advantages of using information on prior batches for analysis and monitoring are often small. Its main advantage is that it can be useful for detecting problems when monitoring new batches in the early stages of their operation., the approach and benefits are illustrated with condensation polymerization and emulsion polymerization systems, as examples. (C) 2004 American Institute of Chemical Engineers.