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Using the effective Lagrangian formalism, the anomalous magnetic and electricdipole moments of the tau-lepton in the $\mu^{+}\mu^{-} \rightarrow\mu^{+}\gamma^{*} \gamma^{*} \mu^{-}\rightarrow \mu^{+}\tau \bar{\tau}\mu^{-}$process at the future muon colliders at the $\sqrt{s}=1.5, 3$ and $6$ TeV areinvestigated. In addition, the bounds at the $95\%$ confidence level on thedipole moments of the tau-lepton using different integrated luminosities areestimated. It is shown that the $\mu^{+}\mu^{-} \rightarrow \mu^{+}\gamma^{*}\gamma^{*} \mu^{-}\rightarrow \mu^{+}\tau \bar{\tau}\mu^{-}$ process leads to aremarkable improvement in the existing experimental bounds on the anomalousmagnetic and electric dipole moments of the tau-lepton.

The $\mu^+\mu^-$ collider to sensitivity estimates on the magnetic and electric dipole moments of the tau-lepton