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We theoretically and experimentally studied the Gilbert damping evolution of both acoustic and optical magnetic resonance modes in the layered flake CrCl3 with an external magnetic field H applied in plane.Based on a Lagrangian equation and a Rayleigh dissipation function,we predicted that the resonance linewidth ΔH as a function of microwave frequency ω is nonlinear for both acoustic and optical modes in the CrC13 flake,which is significantly different from the linear relationship of ΔH ∝ ω in ferromagnets.Measuring the microwave transmission through the CrCl3 flake,we obtained the ω-H dispersion and damping evolution ΔH-ω for both acoustic and optical modes.Combining both our theoretical prediction and experimental observations,we concluded that the nonlinear damping evolution ΔH-ω is a consequence of the interlayer interaction during the antiferromagnetic resonance,and the interlayer Gilbert dissipation plays an important role in the nonlinear damping evolution because of the asymmetry of the non-collinear magnetizaiton between layers.