Histopathological classification of gastric and colonic epithelial tumours is one of the routine pathological diagnosis tasks for pathologists. Computational pathology techniques based on Artificial intelligence (AI) would be of high benefit in easing the ever increasing workloads on pathologists, especially in regions that have shortages in access to pathological diagnosis services. In this study, we trained convolutional neural networks (CNNs) and recurrent neural networks (RNNs) on biopsy histopathology whole-slide images (WSIs) of stomach and colon. The models were trained to classify WSI into adenocarcinoma, adenoma, and non-neoplastic. We evaluated our models on three independent test sets each, achieving area under the curves (AUCs) up to 0.97 and 0.99 for gastric adenocarcinoma and adenoma, respectively, and 0.96 and 0.99 for colonic adenocarcinoma and adenoma respectively. The results demonstrate the generalisation ability of our models and the high promising potential of deployment in a practical histopathological diagnostic workflow system.