The deep learning-based process monitoring method has attracted great attention due to its ability to deal with nonlinear correlation. However, the further modeling of learned deep features from process data to better depict typical process features to obtain more precise monitoring results remains a challenge. In this paper, a novel nonlinear spatiotemporal process feature learning method is proposed to extract high-value slow-varying spatiotemporal process features, with an explicit temporal relationship model for the concurrent monitoring of the static deviation and the dynamic anomaly of complex chemical processes. Different from directly mixed spatiotemporal information methods, the pseudo-Siamese autoencoder network is designed with two different subencoders to separately describe the nonlinear spatial and temporal relationships of the nonlinear dynamic input data. Correspondingly, a cost function including three losses and one orthogonal constraint is proposed to make sure that the extracted spatiotemporal process features change as slowly as possible and contain the most nonlinear dynamic information on the input data. With the explicit spatial and temporal relationship submodel, predictions are utilized to shrink the variability of the nonlinear temporal correlated data and focus on the unpredictable variabilities to improve process monitoring performance. Meanwhile, the linear dynamic information is further extracted in the reconstructed residual space by the general slow feature analysis (SFA) method to provide a more detailed analysis of the process characteristics and improve the monitoring results. The case study monitoring results demonstrate the effectiveness and superiority of the proposed method over other compared methods for concurrent process monitoring.