Text discourse parsing plays an important role in understanding information flow and argumentative structure in natural language. Previous research under the Rhetorical Structure Theory (RST) has mostly focused on inducing and evaluating models from the English treebank. However, the parsing tasks for other languages such as German, Dutch, and Portuguese are still challenging due to the shortage of annotated data. In this work, we investigate two approaches to establish a neural, cross-lingual discourse parser via: (1) utilizing multilingual vector representations; and (2) adopting segment-level translation of the source content. Experiment results show that both methods are effective even with limited training data, and achieve state-of-the-art performance on cross-lingual, document-level discourse parsing on all sub-tasks.