Complete Next to Leading Order QCD Corrections to the Photon Structure Functions $F_2^{\gamma }(x,Q^2)$ and $F_L^{\gamma }(x,Q^2)$

We present the complete NLO QCD analysis of the photon structure functions $F_2^{\gamma }(x,Q^2)$ and $F_L^{\gamma }(x,Q^2)$ for a real photon target. In particular we study the heavy flavor content of the structure functions which is due to two different production mechanisms, namely collisions of a virtual photon with a real photon, and with a parton. We observe that the charm contributions are noticeable for $F_2^{\gamma }(x,Q^2)$ as well as $F_L^{\gamma }(x,Q^2)$ in the x-region studied.