  In this present paper, we investigate the muon pairs production in the
interaction between two quasireal photons in $e^+e^-$ collision. The total and
differential cross section of the process $\gamma \gamma \to \mu^+\mu^-$ at a
beam energy of photons from 3 GeV to 40 GeV in the center-of-mass and for
different values of muon transverse momentum and the muon rapidity and the muon
angle are calculated. We also study the total cross section, as a function of
the $e^+ e^-$ center-of-mass energy $\sqrt {s}$ in the region 5 GeV $\leq \sqrt
{s} \leq$ 209 GeV process of the $e^+ +e^- \to e^+ + e^- +\mu^+ + \mu^-$ by the
two-photon mechanism. The obtained our results are in satisfactory agreement
with the experimental data.
