Multivariate statistical process monitoring (MSPM) methods based on two-dimensional dynamic kernel PCA (2-D-DKPCA) and two-dimensional dynamic kernel Hebbian Algorithm (2-D-DKHA) are proposed. First, a nonlinear batch process monitoring scheme based on 2-D-DKPCA is proposed. Its basic idea is to use KPCA to depict the both within-batch dynamics and batch-to-batch dynamics. However, the proposed 2-D-DKPCA needs to store the whole kernel matrix and calculate all nonlinear components. Kernel matrix will thus become extremely huge when the numbers of successive batches and samples are large. Then, kernel Hebbian Algorithm (KHA) is introduced to 2-D-DKPCA to construct 2-D-DKHA. KHA can extract adaptively nonlinear principal components without storing and manipulating the whole kernel matrix and only calculate the principal components. Thus, proposed 2-D-DKHA has the ability of monitoring complex batch processes. The 2-D-DKPCA and 2-D-DKHA are first proposed in this article. Also, from the proposed 2-D method, it is easily to obtain the 1-D algorithm. The proposed method 2-D-DKPCA is applied to the fault detection in a nonlinear dynamic system and compared with 2-D dynamic PCA (2-D-DPCA). The simulation results show that 2-D-DKPCA is more suitable for nonlinear dynamic process than DPCA. Then the proposed method 2-D-DKHA is applied to penicillin process. The monitoring results show 2-D-DKHA can detect the faults of complex batch process. (C) 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.