The interaction of virtual photons is investigated using the 
reaction e$^+$e$^- \rightarrow$~e$^+$e$^-$hadrons based on data 
taken by the OPAL experiment at e$^+$e$^-$ centre-of-mass 
energies $\sqrt{s_{\mathrm ee}}=189-209$~GeV, for 
$W>5$~GeV and at an average $Q^2$ of 17.9~GeV$^2$.
The measured cross-sections are compared to predictions of the 
Quark Parton Model (QPM), to the Leading Order QCD Monte Carlo
model PHOJET to the NLO prediction for the reaction 
e$^+$e$^- \rightarrow$~e$^+$e$^-$q$\overline{\mathrm q}$, 
and to BFKL calculations. PHOJET, 
NLO e$^+$e$^- \rightarrow$~e$^+$e$^-$q$\overline{\mathrm q}$, and 
QPM describe the data reasonably well, whereas 
the cross-section predicted by a Leading Order BFKL calculation is 
too large.