It is possible to borrow from a topic of biology called phylogenetic systematics, concepts and tools for a logical and objective classification of galaxies. It is based on observable properties of objects - characters - either qualitative (like morphology) or quantitative (like luminosity, mass or spectrum). Distance analysis can readily be performed using a method called phenetics and based on characters. But the most promising approach is cladistics. It makes use of characters that can exist in at least two states, one being "ancestral" and the other one "derived". Objects are gathered depending on the derived states they share. We illustrate the application of this method to astrophysics, that we name "astrocladistics", with dwarf galaxies from the Local Group.