  The photon-induced dimuon production $e^+ e^- \to e^+ \gamma \gamma e^- \to
e^+ \mu^+ \mu^- e^-$ at the CLIC is studied in the framework of three models
with extra dimensions. The electron beam energies 750 GeV and 1500 GeV are
considered. The total cross sections are calculated depending on the minimal
transverse momenta of the final muons. The sensitivity bounds on the parameters
of the models are obtained as functions of the CLIC integrated luminosity.
