Gastrointestinal (GI) diseases are common illnesses that affect the GI tract. Diagnosing these GI diseases is quite expensive, complicated, and challenging. A computer-aided diagnosis (CADx) system based on deep learning (DL) techniques could considerably lower the examination cost processes and increase the speed and quality of diagnosis. Therefore, this article proposes a CADx system called Gastro-CADx to classify several GI diseases using DL techniques. Gastro-CADx involves three progressive stages. Initially, four different CNNs are used as feature extractors to extract spatial features. Most of the related work based on DL approaches extracted spatial features only. However, in the following phase of Gastro-CADx, features extracted in the first stage are applied to the discrete wavelet transform (DWT) and the discrete cosine transform (DCT). DCT and DWT are used to extract temporal-frequency and spatial-frequency features. Additionally, a feature reduction procedure is performed in this stage. Finally, in the third stage of the Gastro-CADx, several combinations of features are fused in a concatenated manner to inspect the effect of feature combination on the output results of the CADx and select the best-fused feature set. Two datasets referred to as Dataset I and II are utilized to evaluate the performance of Gastro-CADx. Results indicated that Gastro-CADx has achieved an accuracy of 97.3% and 99.7% for Dataset I and II respectively. The results were compared with recent related works. The comparison showed that the proposed approach is capable of classifying GI diseases with higher accuracy compared to other work. Thus, it can be used to reduce medical complications, death-rates, in addition to the cost of treatment. It can also help gastroenterologists in producing more accurate diagnosis while lowering inspection time.