  A measurement of the cross section for the combined two-photon production of
charged pion and kaon pairs is performed using 1.2~$\rm fb^{-1}$ of data
collected by the CLEO~II detector at the Cornell Electron Storage Ring. The
cross section is measured at invariant masses of the two-photon system between
1.5 and 5.0 GeV/$c^2$, and at scattering angles more than $53^\circ$ away from
the $\gamma\gamma$ collision axis in the $\gamma\gamma$ center-of-mass frame.
The large background of leptonic events is suppressed by utilizing the CsI
calorimeter in conjunction with the muon chamber system. The reported cross
section is compared with leading order QCD models as well as previous
experiments. In particular, although the functional dependence of the measured
cross section disagrees with leading order QCD at small values of the
two-photon invariant mass, the data show a transition to perturbative behavior
at an invariant mass of approximately 2.5 GeV/$c^2$. hardcopies with figures
can be obtained by writing to to: Pam Morehouse preprint secretary Newman Lab
Cornell University Ithaca, NY 14853 or by sending mail to:
<EMAIL_ADDRESS>