The exclusive production of a proton and an antiproton in the 
collisions of two quasi-real photons has been studied using
data taken at $\sqrt {s_{\mathrm {ee}}} = 183$~GeV and 189~GeV
with the OPAL detector at LEP. Results are presented for
$\gamma\gamma$ invariant masses, $W$, in the range 
$2.15 < W < 3.95$~GeV. The cross-section measurements are 
compared with previous data and with recent analytic 
calculations based on the quark-diquark model.