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We study the sensitivity on the anomalous magnetic and electric dipole moments of the τ-neutrino at a high-energy and high-luminosity linear electron positron collider, such as the ILC or CLIC, through the reaction e+e-→νν̅γ. We obtain limits on the dipole moments at the future linear colliders energies. For integrated luminosities of 500 fb−1 and center of mass energies between 0.5 and 3 TeV, the future e+e- colliders may improve the existing limits by two or three orders of magnitude.