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.
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