We report our multiwavelength observations of two homologous circular-ribbon flares (CRFs) in active region 11991 on 2014 March 5, focusing on the transverse oscillations of an extreme-ultraviolet (EUV) loop excited by the flares. The transverse oscillations are of fast standing kink-mode. The first-stage oscillation triggered by the C2.8 flare is decayless with lower amplitudes (310$-$510 km). The periods (115$-$118 s) in different wavelengths are nearly the same, indicating coherent oscillations. The magnetic field of the loop is estimated to be 65$-$78 G. The second-stage oscillation triggered by the M1.0 flare is decaying with larger amplitudes (1250$-$1280 km). The periods decreases from 117 s in 211 {AA} to 70 s in 171 {AA}, implying a decrease of loop length or an implosion after a gradual expansion. The damping time, being 147$-$315 s, increases with the period, so that the values of $tau/P$ are close to each other in different wavelengths. The thickness of the inhomogeneous layer is estimated to be $sim$0farcs45 under the assumption of resonant absorption. This is the first observation of the excitation of two kink-mode loop oscillations by two sympathetic flares. The results are important for understanding of the excitation of kink oscillations of coronal loops and hence the energy balance in the solar corona. Our findings also validate the prevalence of significantly amplified amplitudes of oscillations by successive drivers.
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