This study aimed to build convolutional neural network (CNN) models capable of classifying upper endoscopy images, to determine the stage of infection in the development of a gastric cancer. Two different problems were covered. A first one with a smaller number of categorical classes and a lower degree of detail. A second one, consisting of a larger number of classes, corresponding to each stage of precancerous conditions in the Correa's cascade. Three public datasets were used to build the dataset that served as input for the classification tasks. The CNN models built for this study are capable of identifying the stage of precancerous conditions/lesions in the moment of an upper endoscopy. A model based on the DenseNet169 architecture achieved an average accuracy of 0.72 in discriminating among the different stages of infection. The trade-off between detail in the definition of lesion classes and classification performance has been explored. Results from the application of Grad CAMs to the trained models show that the proposed CNN architectures base their classification output on the extraction of physiologically relevant image features. Clinical relevance- This research could improve the accuracy of upper endoscopy exams, which have margin for improvement, by assisting doctors when analysing the lesions seen in patient's images.