We investigate the virtual photon structure functions for Λ2 ≪ P2 ≪ Q2, where -Q2 (-P2) is the mass squared of the probe (target) photon. We do this to next-to-leading order in QCD. The non-leading corrections significantly modify the leading log result, in particular at large x. Also, the perturbatively calculated structure function is positive at low x even for P2 ≈ 1 GeV2. (For a real photon target it becomes negative at low x.) For large P2 the QCD result approaches the box diagram (Born) structure function also when non-leading contributions are included. It is, however, important to include the large non-leading box diagram contributions in making this comparison.