Deep Learning has been very successful in many application domains. However, its usefulness in the context of network intrusion detection has not been systematically investigated. In this paper, we report a case study on using deep learning for both supervised network intrusion detection and unsupervised network anomaly detection. We show that Deep Neural Networks (DNNs) can outperform other machine learning based intrusion detection systems, while being robust in the presence of dynamic IP addresses. We also show that Autoencoders can be effective for network anomaly detection.