Multi-label classification is the task of predicting a set of labels for a given input instance. Classifier chains are a state-of-the-art method for tackling such problems, which essentially converts this problem into a sequential prediction problem, where the labels are first ordered in an arbitrary fashion, and the task is to predict a sequence of binary values for these labels. In this paper, we replace classifier chains with recurrent neural networks, a sequence-to-sequence prediction algorithm which has recently been successfully applied to sequential prediction tasks in many domains. The key advantage of this approach is that it allows to focus on the prediction of the positive labels only, a much smaller set than the full set of possible labels. Moreover, parameter sharing across all classifiers allows to better exploit information of previous decisions. As both, classifier chains and recurrent neural networks depend on a fixed ordering of the labels, which is typically not part of a multi-label problem specification, we also compare different ways of ordering the label set, and give some recommendations on suitable ordering strategies.