Housing structure (100, 200) for a fluid-flow machine, in particular for a turbomachine, the housing structure (100, 200) being designed to annularly surround, at least in part, a main flow channel of the fluid-flow machine, in which rotor blades and stator blades are arranged, and to delimit the fluid-flow machine from the surroundings, the housing structure (100, 200) having an outer housing wall formed by at least one housing part and an inner wall and comprising at least one cooling air channel, extending at least in part in a volume between the housing wall and the inner wall, for cooling a housing portion of the housing wall to be cooled, - the housing wall being designed to delimit the fluid-flow machine from the surroundings, - the inner wall being arranged in the radial direction (r) inside the housing wall and in the radial direction (r) at a distance from the housing wall and being designed to delimit, at least in part, the main flow channel having the rotor blades and stator blades arranged therein, - the housing portion to be cooled having an upstream end and a downstream end in relation to a main flow direction in which a main flow flows through the main flow channel, - the cooling air channel having a cooling air channel inlet for supplying cooling air into the cooling air channel and a cooling air channel outlet for discharging cooling air from the cooling air channel, and - the cooling air channel having a first portion and a second portion, the housing structure (100, 200) being designed such that cooli ng air supplied to the cooling air channel via the cooling air channel inlet flows, in the first portion, in the direction of the upstream end of the housing portion to be cooled and, in the second portion, in the direction of the downstream end of the housing portion to be cooled, a cooling air flow being deflected in the transition from the first portion to the second portion, the cooling air channel inlet being arranged in the region of the downstream end of the housing portion to be cooled or downstream thereof, characterized in that the housing structure (100, 200) comprises at least two partition walls (Z1, Z2), specifically a first partition wall and a second partition wall, extending at least in part in the axial direction (a) and at least in part in the circumferential direction and arranged in the radial direction (r) between the housing wall and the inner wall, the cooling air channel being delimited in the first portion in the radial direction by an inner surface of the housing portion of the housing wall to be cooled and by an outer surface of the first partition wall arranged in the radial direction (r) between the housing wall and the inner wall, the cooling air channel being delimited in the second portion outward in the radial direction by an inner surface of the first partition wall and inward in the radial direction (r) by an outer surface of the second partition wall arranged in the radial direction (r) between the first partition wall and the inner wall. - the housing wall being designed to delimit the fluid-flow machine from the surroundings, - the inner wall being arranged in the radial direction (r) inside the housing wall and in the radial direction (r) at a distance from the housing wall and being designed to delimit, at least in part, the main flow channel having the rotor blades and stator blades arranged therein, - the housing portion to be cooled having an upstream end and a downstream end in relation to a main flow direction in which a main flow flows through the main flow channel, - the cooling air channel having a cooling air channel inlet for supplying cooling air into the cooling air channel and a cooling air channel outlet for discharging cooling air from the cooling air channel, and - the cooling air channel having a first portion and a second portion, the housing structure (100, 200) being designed such that cooli ng air supplied to the cooling air channel via the cooling air channel inlet flows, in the first portion, in the direction of the upstream end of the housing portion to be cooled and, in the second portion, in the direction of the downstream end of the housing portion to be cooled, a cooling air flow being deflected in the transition from the first portion to the second portion,