Semileptonic decays of b hadrons into muons were used to measure
the total cross section for open beauty production in 
photon-photon collisions with the OPAL experiment at LEP
at e$^+$e$^-$ centre-of-mass energies
$\sqrt {s_{\mathrm {ee}}} = 189 - 202$~GeV. The production 
cross section was determined to be 
$\sigma ({\mathrm e}^+{\mathrm e}^- \rightarrow 
{\mathrm e}^+{\mathrm e}^-{\mathrm b}\overline{\mathrm b})
= 14.2 \pm 2.5~{\mathrm {(stat)}}~^{-4.8}_{+5.3}~{\mathrm {(sys)}}$~pb
which is about 2 standard deviations higher than expected from 
a perturbative next-to-leading order QCD calculation.