Coronary artery disease leading up to stenosis, the partial or total blocking of coronary arteries, is a severe condition that affects millions of patients each year. Automated identification and classification of stenosis severity from minimally invasive procedures would be of great clinical value, but existing methods do not match the accuracy of experienced cardiologists, due to the complexity of the task. Although a number of computational approaches for quantitative assessment of stenosis have been proposed to date, the performance of these methods is still far from the required levels for clinical applications. In this paper, we propose a two-step deep-learning framework to partially automate the detection of stenosis from X-ray coronary angiography images. In the two steps, we used two distinct convolutional neural network architectures, one to automatically identify and classify the angle of view, and another to determine the bounding boxes of the regions of interest in frames where stenosis is visible. Transfer learning and data augmentation techniques were used to boost the performance of the system in both tasks. We achieved a 0.97 accuracy on the task of classifying the Left/Right Coronary Artery (LCA/RCA) angle view and 0.68/0.73 recall on the determination of the regions of interest, for LCA and RCA, respectively. These results compare favorably with previous results obtained using related approaches, and open the way to a fully automated method for the identification of stenosis severity from X-ray angiographies.