We find four-dimensional black hole solutions of the tree-level string effective action, that carry both electric and magnetic charge. The solutions involve non-trivial axion and dilaton fields, and are related to one another by a form of duality transformation. These black holes have drastically different global properties from the usual charged holes without axions and dilatons. The global causal structures of the effective metrics seen by different types of particles (for the same solution) can differ.