Improving machine translation (MT) by learning from human post-edits is a powerful solution that is still unexplored in the neural machine translation (NMT) framework. Also in this scenario, effective techniques for the continuous tuning of an existing model to a stream of manual corrections would have several advantages over current batch methods. First, they would make it possible to adapt systems at run time to new users/domains; second, this would happen at a lower computational cost compared to NMT retraining from scratch or in batch mode. To attack the problem, we explore several online learning strategies to stepwise fine-tune an existing model to the incoming post-edits. Our evaluation on data from two language pairs and different target domains shows significant improvements over the use of static models.