Languages evolve and diverge over time. Their evolutionary history is often depicted in the shape of a phylogenetic tree. Assuming parsing models are representations of their languages grammars, their evolution should follow a structure similar to that of the phylo-genetic tree. In this paper, drawing inspiration from multi-task learning, we make use of the phylogenetic tree to guide the learning of multilingual dependency parsers leverag-ing languages structural similarities. Experiments on data from the Universal Dependency project show that phylogenetic training is beneficial to low resourced languages and to well furnished languages families. As a side product of phylogenetic training, our model is able to perform zero-shot parsing of previously unseen languages.