  The parametrisation of the photon structure function in the low Q^2 region is
formulated. It includes the VMD contribution and the QCD improved parton model
component suitably extrapolated to the low Q^2 region. The parametrisation
describes reasonably well existing experimental data on sigma_{\gamma \gamma}
for real photons and the low Q^2 data on sigma_{\gamma^* \gamma}. Predictions
for sigma_{\gamma \gamma} and for sigma_{\gamma^* \gamma} for energies which
may be accesssible in future linear colliders are also given.
