Deep two-dimensional (2-D) convolutional neural networks (CNNs) have been remarkably successful in producing record-breaking results in a variety of computer vision tasks. It is possible to extend CNNs to three dimensions using 3-D kernels to make them suitable for volumetric medical imaging data such as CT or MRI, but this increases the processing time as well as the required number of training samples (due to the higher number of parameters that need to be learned). In this paper, we address both of these issues for a 3-D CNN implementation through the development of a two-stage computer-aided detection system for automatic detection of pulmonary nodules. The first stage consists of a 3-D fully convolutional network for fast screening and generation of candidate suspicious regions. The second stage consists of an ensemble of 3-D CNNs trained using extensive transformations applied to both the positive and negative patches to augment the training set. To enable the second stage classifiers to learn differently, they are trained on false positive patches obtained from the screening model using different thresholds on their associated scores as well as different augmentation types. The networks in the second stage are averaged together to produce the final classification score for each candidate patch. Using this procedure, our overall nodule detection system called DeepMed is fast and can achieve 91% sensitivity at 2 false positives per scan on cases from the LIDC dataset.