The batch process generally covers high nonlinearity and two-directional dynamics: time-wise dynamics, which correspond to inherently time-varying dynamics resulting from the slowly varying underlying driving forces within each batch duration; and batch-wise dynamics, which are associated with different operating modes among different batches. However, most existing dynamic nonlinear monitoring methods cannot extract the slowly varying underlying driving forces of the nonlinear batch process and rarely tackle the batch-wise dynamic characteristics among batch runs. In order to address these issues, a new monitoring scheme based on two-directional dynamic kernel slow feature analysis (TDKSFA) is developed by combining kernel SFA with a global modelling strategy. In the TDKSFA method, kernel SFA is integrated with the ARMAX time series model to mine the nonlinear and time-wise dynamic properties within a batch run due to its capability of extracting the slowly varying underlying driving forces. Furthermore, the global modelling strategy is presented to handle the batch-wise dynamics among batches by calculating the total average kernel matrix of all training batches. After the slow features are extracted, Hotelling'sT(2)andSPEstatistics are built to detect faults. To solve the issue of fault variable nonlinear identification, a novel nonlinear contribution plot inspired by the pseudo-sample variable projection trajectories in the TDKSFA model is further proposed to identify fault variables. Finally, the feasibility and effectiveness of the TDKSFA-based fault diagnosis strategy is demonstrated through a numerical system and the penicillin fermentation process.