We investigate some of the theoretical questions which can be studied in the reaction e + e → e + e + hadrons where the electrons are scattered with large momentum transfer. The even charge conjugation part of this reaction is determined by the off-mass shell behaviour of the amplitude γ* + γ* → hadrons. At fixed hadron mass, there exists a scaling relation for this amplitude in terms of the virtual photon masses. When the hadron mass becomes large, parton models and bilocal algebras yield definite predictions for the absorptive part of the forward virtual photon-photon scattering amplitude. The colliding beam cross sections which result are of order 10-36 cm2.