  The forward elastic amplitude for scattering of real and weakly virtual
photons is studied in the framework of the theory of reggeized gluons, with
large $N_{c}$ and a running coupling constant introduced in the manner which
preserves the bootstrap condition. Transition from a single to multiple pomeron
exchanges is observed as $x$ gets smaller. For very low $x$ the amplitude
aquires an eikonal form. The photon structure function reveals a strong
violation of scaling: it grows as $Q^{2}$. As a function of $x$ it behaves as
$(\ln(1/x)\ln\ln(1/x))^{2}$. Correspondingly the cross-section for physical
photons grows with energy as $(\ln s\ln\ln s)^{2}$. Hadronic structure
functions and cross-sections are also briefly discussed.
