We develop and evaluate a deep learning algorithm to classify multiple catheters on neonatal chest and abdominal radiographs. A convolutional neural network (CNN) was trained using a dataset of 777 neonatal chest and abdominal radiographs, with a split of 81%-9%-10% for training-validation-testing, respectively. We employed ResNet-50 (a CNN), pre-trained on ImageNet. Ground truth labelling was limited to tagging each image to indicate the presence or absence of endotracheal tubes (ETTs), nasogastric tubes (NGTs), and umbilical arterial and venous catheters (UACs, UVCs). The data set included 561 images containing 2 or more catheters, 167 images with only one, and 49 with none. Performance was measured with average precision (AP), calculated from the area under the precision-recall curve. On our test data, the algorithm achieved an overall AP (95% confidence interval) of 0.977 (0.679-0.999) for NGTs, 0.989 (0.751-1.000) for ETTs, 0.979 (0.873-0.997) for UACs, and 0.937 (0.785-0.984) for UVCs. Performance was similar for the set of 58 test images consisting of 2 or more catheters, with an AP of 0.975 (0.255-1.000) for NGTs, 0.997 (0.009-1.000) for ETTs, 0.981 (0.797-0.998) for UACs, and 0.937 (0.689-0.990) for UVCs. Our network thus achieves strong performance in the simultaneous detection of these four catheter types. Radiologists may use such an algorithm as a time-saving mechanism to automate reporting of catheters on radiographs.