In this paper, a new process monitoring approach is proposed for multimode time-varying processes. The Kronecker product is introduced to modify the monitoring matrices. Then the original space can be separated into two different parts, which are the common part and the specific part. There are both time-varying similarity and dissimilarity in the underlying correlations of different modes, which play different roles in the industrial processes. Because the industrial processes have the non-Gaussian and nonlinear characteristics, the kernel independent component analysis (KICA) is modified to monitor the multimode time-varying processes in this paper. The global multimode basis vector and the multimode sub-basis vector are obtained based on the modified KICA. Then, the common part and specific part in one mode are, respectively, analyzed. The proposed method is applied to monitor the continuous annealing process. The proposed approach effectively extracts the non-Gaussian and nonlinear features in the different time-varying modes. (C) 2012 Elsevier Ltd. All rights reserved.