This paper proposes a fast and reliable method for anomaly detection and localization in video data showing crowded scenes. Time-efficient anomaly localization is an ongoing challenge and subject of this paper. We propose a cubicpatch- based method, characterised by a cascade of classifiers, which makes use of an advanced feature-learning approach. Our cascade of classifiers has two main stages. First, a light but deep 3D auto-encoder is used for early identification of "many" normal cubic patches. This deep network operates on small cubic patches as being the first stage, before carefully resizing remaining candidates of interest, and evaluating those at the second stage using a more complex and deeper 3D convolutional neural network (CNN). We divide the deep autoencoder and the CNN into multiple sub-stages which operate as cascaded classifiers. Shallow layers of the cascaded deep networks (designed as Gaussian classifiers, acting as weak single-class classifiers) detect "simple" normal patches such as background patches, and more complex normal patches are detected at deeper layers. It is shown that the proposed novel technique (a cascade of two cascaded classifiers) performs comparable to current top-performing detection and localization methods on standard benchmarks, but outperforms those in general with respect to required computation time.