Multiway principal component analysis (MPCA) for the analysis and monitoring of batch processes has recently been proposed. Although MPCA has found wide applications in batch process monitoring, it assumes that future batches behave in the same way as those used for model identification. In this study, a new monitoring algorithm, adaptive multiblock MPCA, is developed. The method overcomes the problem of changing process conditions by updating the covariance structure recursively. A historical set of operational data of a multiphase batch process was divided into local blocks in such a way that the variables from one phase of a batch run could be blocked in the corresponding blocks. This approach has significant benefits because the latent variable structure can change for each phase during the batch operation. The adaptive multiblock model also allows for easier fault detection and isolation by looking at the relationship between blocks and at smaller meaningful block models, and it therefore helps in the diagnosis of the disturbance. The proposed adaptive multiblock monitoring method is successfully applied to a sequencing batch reactor for biological wastewater treatment. © 2003 Wiley Periodicals, Inc. Biotechnol Bioeng 82: 489–497, 2003.