Di-jet production is studied in collisions of quasi-real photons radiated
by the LEP beams at e$^+$e$^-$ centre-of-mass energies from 189 to 209 GeV. 
The data have been taken with the OPAL detector. Jets are reconstructed using
a $k_t$-clustering and a cone algorithm. The jet structure is studied in
terms of the jet shape $\Psi(r)$. Angular distributions in di-jet events are
measured and used to demonstrate the dominance of quark and gluon
initiated processes in different regions of phase space.  The inclusive
di-jet cross-section is measured as a function of the mean transverse
energy $E_T^{\mathrm {jet}}(mean)$ of the two jets, and as a function of the 
estimated
fraction of the photon momentum carried by the parton entering the hard
sub-process, $x_\gamma$, for different regions of 
$E_T^{\mathrm{jet}}(mean)$. Furthermore the
inclusive di-jet cross-section as a function of |$\eta^{\mathrm{jet}}$| and
|$\delta(\eta^{\mathrm{jet}})$| is presented, where 
$\eta_{\mathrm{jet}}$ is the jet pseudo-rapidity. 
Different regions of the $x_\gamma^+$-$x_\gamma^-$ space are explored 
to study and control
the influence of a possible underlying event.  The results are compared to
next-to-leading order perturbative QCD calculations.