Testing QCD: Direct photons in e⁺e^- collisions

We discuss QCD predictions for the production of direct photons in e⁺e^- collisions, e⁺e^-→ γ^*→γ+ hadrons (C=+). A simple derivation of the QCD results for the structure functions is presented. These turn out to be exactly predicted by the theory, in contrast to hadron production where only the change with Q² is predictable. We also take up the phenomenology of this process. A dramatic rise of the γ/π⁰ ratio with z=E_γ/E_B(E_π/E_B) and with Q² is predicted.