We introduce a Language-consistent multi-lingual Open Relation Extraction Model (LOREM) for finding relation tuples of any type between entities in unstructured texts. LOREM does not rely on language-specific knowledge or external NLP tools such as translators or PoS-taggers, and exploits information and structures that are consistent over different languages. This allows our model to be easily extended with only limited training efforts to new languages, but also provides a boost to performance for a given single language. An extensive evaluation performed on 5 languages shows that LOREM outperforms state-of-the-art mono-lingual and cross-lingual open relation extractors. Moreover, experiments on languages with no or only little training data indicate that LOREM generalizes to other languages than the languages that it is trained on.