Many real world problems involve data which can be considered as multi-label data streams. Efficient methods exist for multi-label classification in non streaming scenarios. However, learning in evolving streaming scenarios is more challenging, as the learners must be able to adapt to change using limited time and memory. This paper proposes a new experimental framework for studying multi-label evolving stream classification, and new efficient methods that combine the best practices in streaming scenarios with the best practices in multi-label classification. We present a Multi-label Hoeffding Tree with multilabel classifiers at the leaves as a base classifier. We obtain fast and accurate methods, that are well suited for this challenging multi-label classification streaming task. Using the new experimental framework, we test our methodology by performing an evaluation study on synthetic and real-world datasets. In comparison to well-known batch multi-label methods, we obtain encouraging results.