Various types of atherosclerotic plaque and varying grades of stenosis could lead to different management of patients with a coronary artery disease. Therefore, it is crucial to detect and classify the type of coronary artery plaque, as well as to detect and determine the degree of coronary artery stenosis. This paper includes retrospectively collected clinically obtained coronary CT angiography (CCTA) scans of 163 patients. In these, the centerlines of the coronary arteries were extracted and used to reconstruct multi-planar reformatted (MPR) images for the coronary arteries. To define the reference standard, the presence and the type of plaque in the coronary arteries (no plaque, non-calcified, mixed, calcified), as well as the presence and the anatomical significance of coronary stenosis (no stenosis, non-significant, i.e., <50% luminal narrowing, and significant, i.e., ≥50% luminal narrowing) were manually annotated in the MPR images by identifying the start- and end-points of the segment of the artery affected by the plaque. To perform an automatic analysis, a multi-task recurrent convolutional neural network is applied on coronary artery MPR images. First, a 3D convolutional neural network is utilized to extract features along the coronary artery. Subsequently, the extracted features are aggregated by a recurrent neural network that performs two simultaneous multi-class classification tasks. In the first task, the network detects and characterizes the type of the coronary artery plaque. In the second task, the network detects and determines the anatomical significance of the coronary artery stenosis. The network was trained and tested using the CCTA images of 98 and 65 patients, respectively. For detection and characterization of coronary plaque, the method was achieved an accuracy of 0.77. For detection of stenosis and determination of its anatomical significance, the method was achieved an accuracy of 0.80. The results demonstrate that automatic detection and classification of coronary artery plaque and stenosis are feasible. This may enable automated triage of patients to those without coronary plaque and those with coronary plaque and stenosis in need for further cardiovascular workup.