Blue whales (Balaenoptera musculus) and fin whales (Balaenoptera physalus) are closely related species that have both experienced declines in population size. The vocalizations of these species provide data on populations sizes and migratory patterns, but the similarity of a subset of their vocalizations presents issues for automated processing. The seasonal variation, proximity to feeding areas, and correlation with feeding behaviors provide evidence that both the blue whale D calls and fin whale 40-Hz calls are feeding-specific calls. The overlapping frequency ranges and frequency modulated nature of the calls, the common genetic background of the two species, and the similar function of the calls are possible contributors to the difficulties in the detection and accurate classification of these calls. Detectors which target downswept call types within this frequency range will experience high recall of both blue whale D calls and fin whale 40-Hz calls, which would require further human annotation to classify each. Building on the success of using deep neural networks for the detection of low-frequency whale calls and for the classification of high-frequency whale vocalizations, we adapt Caffe's freely available AlexNet implementation to tackle the task of distinguishing between blue whale D calls and fin whale 40Hz calls. We obtained over 1387 hours of audio taken from passive acoustic monitoring recorded between 2009-2013 off the coast of Southern California. Ground truth annotation by human experts provided 4796 D calls and 415 40-Hz calls. Using spectrograms of these vocalizations, we extracted high level features from our network and trained an SVM classifier to predict the call type. Our system achieved an overall 97.6% classification accuracy with a 98.6% precision and 98.8% recall for blue whale D calls. Augmenting current blue whale D call detection methods with an additional classification step will allow researchers to eliminate fin whale 40-Hz calls and move through their data faster. Additionally, this method is very flexible and allows researchers the ability to add additional call types to pursue more fine-grained classifiers.