A method which for the first time can treat two truly semi-infinite semiconductors in contact is introduced and used to study the electronic structure of the two polar (100) Ge-GaAs interfaces. Both the Ge-Ga and the Ge-As interfaces exhibit essentially three interface bands. The nature and origins of these bands are discussed in detail in terms of local densities of states. The results are used to obtain a new interpretation of the experimental data in terms of a stoichiometrically mixed interface. © 1979.