A gas turbine combustor comprising: a combustor basket in which combustion gas flows in operation, the combustion gas being produced by combustion of fuel injected from at least one nozzle (2,3); a first resonance device for damping combustion oscillation, the first resonance device being mounted on an outer surface of the combustor basket; a transition piece for introducing the combustion gas produced in the combustor basket to a turbine, the transition piece being arranged so that an upstream end of the transition piece overlaps an outer periphery of a downstream end of the combustor basket; and a second resonance device for damping combustion oscillation of a frequency higher than the first resonance device, the second resonance device being mounted on the outer surface of the combustor basket so as to be disposed on a downstream side from the first resonance device in a flow of the combustion gas, wherein the first resonance device and the second resonance device are acoustic liners each having a housing (12;22) mounted to the outer surface of the combustor basket, wherein a resonance space (14;24) surrounded by the respective housing (12;22) and the outer surface of the combustor basket has a respective height and communicates with an interior space of the combustor basket via a plurality of acoustic holes (16;26) formed in the combustor basket, wherein the resonance space of the second resonance device has the height h 2 smaller than the height h 1 of the resonance space of the first resonance device, and wherein the second resonance device is arranged in an area where the transition piece overlaps the combustor basket. a combustor basket in which combustion gas flows in operation, the combustion gas being produced by combustion of fuel injected from at least one nozzle (2,3); a first resonance device for damping combustion oscillation, the first resonance device being mounted on an outer surface of the combustor basket; a transition piece for introducing the combustion gas produced in the combustor basket to a turbine, the transition piece being arranged so that an upstream end of the transition piece overlaps an outer periphery of a downstream end of the combustor basket; and a second resonance device for damping combustion oscillation of a frequency higher than the first resonance device, the second resonance device being mounted on the outer surface of the combustor basket so as to be disposed on a downstream side from the first resonance device in a flow of the combustion gas, wherein the first resonance device and the second resonance device are acoustic liners each having a housing (12;22) mounted to the outer surface of the combustor basket, wherein a resonance space (14;24) surrounded by the respective housing (12;22) and the outer surface of the combustor basket has a respective height and communicates with an interior space of the combustor basket via a plurality of acoustic holes (16;26) formed in the combustor basket, wherein the resonance space of the second resonance device has the height h 2 smaller than the height h 1 of the resonance space of the first resonance device, and wherein the second resonance device is arranged in an area where the transition piece overlaps the combustor basket.