This paper presents a new approach to the problem of cross-lingual dependency parsing, aiming at leveraging training data from different source languages to learn a parser in a target language. Specifically , this approach first constructs word vector representations that exploit structural (i.e., dependency-based) contexts but only considering the morpho-syntactic information associated with each word and its contexts. These delexicalized word em-beddings, which can be trained on any set of languages and capture features shared across languages, are then used in combination with standard language-specific features to train a lexicalized parser in the target language. We evaluate our approach through experiments on a set of eight different languages that are part the Universal Dependencies Project. Our main results show that using such delexicalized embeddings, either trained in a monolin-gual or multilingual fashion, achieves significant improvements over monolingual baselines.