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We investigate the virtual effects of vector unparticles in the Mollerscattering. We derive the analytic expression for scattering amplitudes withunpolarized beams. We obtain 95% confidence level limits on the unparticlecouplings $\lambda_{V}$ and $\lambda_{A}$ with integrated luminosity of$L_{int}=50, 500 fb^{-1}$ and $\sqrt{s}=100, 300$ and 500 GeV energies. We showthat limits on $\lambda_{V}$ are more sensitive than $\lambda_{A}$.

Unparticle Physics in the Moller Scattering