A gas turbine that comprises: a combustor coupled to a turbine that together define a working fluid flowpath, the working fluid flowpath extending aftward along a longitudinal axis from a forward end defined by a forward injector in the combustor, through an interface at which the combustor transitions to the turbine, and then through the turbine to an aftward end defined therein, wherein the combustor includes an inner radial wall, which defines the working fluid flowpath, and an outer radial wall, which is formed about the inner radial wall such that a flow annulus is formed therebetween; a compressor discharge cavity formed about the combustor for receiving a combustor air supply delivered thereto by a compressor; a staged injection system that includes the forward injector and, axially spaced aftward therefrom, a staged injector, wherein the staged injector intersects the flow annulus so to attain an injection point within the working fluid flowpath, and wherein, relative an axial position of the injection point, an aftward annulus section is defined to an aftward side of the injection point and a forward annulus section is defined to a forward side of the injection point; fuel directing structure for apportioning a combustor fuel supply between the forward injector and the staged injector; and air directing structure for apportioning the combustor air supply between the forward injector and the staged injector; wherein the air directing structure comprises axially defined intake sections formed through the outer radial wall that fluidly connect the compressor discharge cavity to corresponding axially defined sections of the flow annulus characterized in that, the intake sections includes an aftward intake section that corresponds to the aftward annulus section and a forward intake section that corresponds to the forward annulus section; and the air directing structure is configured to: direct air entering through the aftward intake section through the aftward annulus section in a forward direction to the staged injector; and direct air entering through the forward intake section through the forward annulus section in an aftward direction to the staged injector. a combustor coupled to a turbine that together define a working fluid flowpath, the working fluid flowpath extending aftward along a longitudinal axis from a forward end defined by a forward injector in the combustor, through an interface at which the combustor transitions to the turbine, and then through the turbine to an aftward end defined therein, wherein the combustor includes an inner radial wall, which defines the working fluid flowpath, and an outer radial wall, which is formed about the inner radial wall such that a flow annulus is formed therebetween; a compressor discharge cavity formed about the combustor for receiving a combustor air supply delivered thereto by a compressor; a staged injection system that includes the forward injector and, axially spaced aftward therefrom, a staged injector, wherein the staged injector intersects the flow annulus so to attain an injection point within the working fluid flowpath, and wherein, relative an axial position of the injection point, an aftward annulus section is defined to an aftward side of the injection point and a forward annulus section is defined to a forward side of the injection point; fuel directing structure for apportioning a combustor fuel supply between the forward injector and the staged injector; and air directing structure for apportioning the combustor air supply between the forward injector and the staged injector; direct air entering through the aftward intake section through the aftward annulus section in a forward direction to the staged injector; and direct air entering through the forward intake section through the forward annulus section in an aftward direction to the staged injector.