A gas turbine combustor comprising: a plurality of combustors each including a partition wall constituting a combustion chamber, and an outer peripheral partition wall provided at an outer periphery of the partition wall and defining a combustion air flow passage between itself and the partition wall ; and a crossfire tube assembly connecting adjacent ones of the plurality of combustors , the crossfire tube assembly including an inner tube that connects the partition walls of the adjacent combustors , and an outer tube that is provided at an outer periphery of the inner tube and connects the outer peripheral partition walls of the adjacent combustors , the inner tube being divided in an axial direction into a first inner tube member and a second inner tube member , an end portion of the second inner tube member on the first inner tube member side having an enlarged portion that has an inside diameter (Db) greater than an outside diameter (Da) of the first inner tube member , and the first inner tube member and the second inner tube member forming a fitting portion such that part of the first inner tube member is located on an inner periphery side of the enlarged portion of the second inner tube member with a gap therebetween, characterized in that a sectional shape in a radial direction of either one of an inner peripheral surface of the second inner tube member and an outer peripheral surface of the first inner tube member at the fitting portion has a plurality of small-curvature portions on the peripheral surface of the second inner tube member or the peripheral surface of the first inner tube member , each of the plurality of small-curvature portions having a curvature smaller than a reference curvature, wherein the reference curvature is the curvature at the portion where the distance from the center of the sectional shape is at a maximum, and wherein the reference curvature is defined by the reciprocal of said maximum distance. a plurality of combustors each including a partition wall constituting a combustion chamber, and an outer peripheral partition wall provided at an outer periphery of the partition wall and defining a combustion air flow passage between itself and the partition wall ; and a crossfire tube assembly connecting adjacent ones of the plurality of combustors , the crossfire tube assembly including an inner tube that connects the partition walls of the adjacent combustors , and an outer tube that is provided at an outer periphery of the inner tube and connects the outer peripheral partition walls of the adjacent combustors , the inner tube being divided in an axial direction into a first inner tube member and a second inner tube member , an end portion of the second inner tube member on the first inner tube member side having an enlarged portion that has an inside diameter (Db) greater than an outside diameter (Da) of the first inner tube member , and the first inner tube member and the second inner tube member forming a fitting portion such that part of the first inner tube member is located on an inner periphery side of the enlarged portion of the second inner tube member with a gap therebetween, characterized in that a sectional shape in a radial direction of either one of an inner peripheral surface of the second inner tube member and an outer peripheral surface of the first inner tube member at the fitting portion has a plurality of small-curvature portions on the peripheral surface of the second inner tube member or the peripheral surface of the first inner tube member , each of the plurality of small-curvature portions having a curvature smaller than a reference curvature, wherein the reference curvature is the curvature at the portion where the distance from the center of the sectional shape is at a maximum, and wherein the reference curvature is defined by the reciprocal of said maximum distance. <EOS>