Multivariate statistical procedures for monitoring the behavior of batch processes are presented. A Mew type of regression, called multiway covariates regression, ir used Co Sind the relationship between the process variables and the quality variables of the final product. The three-way structure of the batch process data is modeled by means of a Tucker3 or a PARAFAC model. The only information needed is a historical data set of past successful batches. Subsequent new batches can be monitored using multivariate statistical process control charts. In this way the progress of the new batch can be tracked and possible faults can be easily detected. Further detailed information from the process can be obtained by interrogating the underlying model. Diagnostic tools, such as contribution plots of each of the variables to the observed deviation, are also developed. Finally, on-line predictions of the final quality variables can be monitored; providing an additional tool to see whether a particular batch will produce an out-of-spec product. These ideas are illustrated using simulated and real data of a batch polymerization reaction.