Inclusive ${\mathrm{ D^{*\pm}}}$ production in two-photon 
collisions is studied with the 
L3 detector at LEP, using 683 $\mathrm{pb^{-1}}$
of data collected at centre-of-mass energies from 183 to 208 GeV. 
Differential cross sections are determined as functions 
of the transverse momentum and 
pseudorapidity of the ${\mathrm{ D^{*\pm}}}$ mesons in the kinematic 
region ${1~\mathrm{GeV} < P_T < 12~\mathrm{GeV}}$ 
and ${\vert \eta \vert < 1.4}$. 
The cross sections
 $ \sigma({\mathrm{ e^{+}e^{-} \rightarrow e^{+}e^{-}D^{*\pm}X}})$ 
in this kinematical region is measured and 
the $\sigma({\mathrm{ e^{+}e^{-} \rightarrow e^{+}e^{-}c\bar{c}X}})$
cross section is derived. The measurements are compared with 
next-to-leading order perturbative QCD calculations.