The structure functions of real and virtual photons are derived from cross section measurements of the reaction e e qy qy ae e q hadrons at LEP. The reaction is studied at 's ,91 GeV with the L3 detector. One of the final state electrons is detected at a large angle relative to the beam direction, leading to Q2 values between 40 GeV2 and 500 GeV2. The other final state electron is either undetected or it is detected at a four-momentum transfer squared P2 between 1 GeV2 and 8 GeV2 . These measurements are compared with predictions of the Quark Parton Model and other QCD based models.