Reliable online quality prediction of sequential-reactor-multi-grade (SRMG) chemical processes often encounters different challenges, including process nonlinearity, input variable selection/extraction, sequential relationship in reactors, and multiple grades in a production line. A novel just-in-time sequential nonlinear modeling method is proposed. It integrates input variable selection/extraction and quality prediction into a unified framework. First, the input variables in the previous reactors are substituted by "virtual" quality variables via least squares support vector regression (LSSVR) transform models. Then, the sequential relationship in a sequential reactor process can be captured by a global sequential LSSVR model using an efficient training strategy. Furthermore, for a new Lest sample, an improved model is constructed by integrating just-in-Lime learning and the proposed sequential LSSVR model. Consequently, shifting into operating modes for multiple grades can perform better than a single global model. Finally, the proposed just-in-Lime sequential LSSVR (JS-LSSVR) model shows sequential, global-local, and quality-relevant characteristics for an SRMG process. The JS-LSSVR modeling method is applied to online prediction of melt index in an industrial polymerization production process in Taiwan. The prediction results show its superiority in terms of high prediction accuracy and reliability in comparison with other approaches. (C) 2013 Elsevier Ltd. All rights reserved.