The ability to proactively monitor business processes is a main competitive differentiator for firms. Process execution logs generated by process aware information systems help to make process specific predictions for enabling a proactive situational awareness. The goal of the proposed approach is to predict the next process event from the completed activities of the running process instance, based on the execution log data from previously completed process instances. By predicting process events, companies can initiate timely interventions to address undesired deviations from the desired workflow. The paper proposes a multi-stage deep learning approach that formulates the next event prediction problem as a classification problem. Following a feature pre-processing stage with n-grams and feature hashing, a deep learning model consisting of an unsupervised pre-training component with stacked autoencoders and a supervised fine-tuning component is applied. Experiments on a variety of business process log datasets show that the multi-stage deep learning approach provides promising results. The study also compared the results to existing deep recurrent neural networks and conventional classification approaches. Furthermore, the paper addresses the identification of suitable hyperparameters for the proposed approach, and the handling of the imbalanced nature of business process event datasets.