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Gilbert's damping constants, α , of Co-Cr-Ta and Co-Cr-Pt thin films are determined by Q-band FMR analysis using single crystal magnetic thin films epitaxialIy grown on MgO(110) substrates. α is calculated from the resonance width of the FMR spectrum. α of Co77Cr19Ta4 is found to increase from 0.016 to 0.028 as magnetic layer thickness increases from 25 to 240 nm. α also increases from 0.009 to 0.019 when the Cr concentration in the 60 nm thick Co96-x CrxTa4 magnetic layer is increased from 8 to 19 at.%. The 25 nm thick Co81Cr15Pt4, film has a 2.5 times larger α value (0.038) than the Co81Cr15Ta4 film (α = 0.014) with the same thickness.