A gas turbine engine, comprising: a primary gas path having, in fluid series communication: a primary air inlet, a compressor fluidly connected to the primary air inlet, a combustor fluidly connected to an outlet of the compressor, and a turbine fluidly connected to an outlet of the combustor, the turbine operatively connected to the compressor to drive the compressor; and a turbine cooling air conduit extending from an air inlet of the turbine cooling air conduit to an air outlet of the turbine cooling air conduit, the upstream air inlet connected in fluid communication with the primary gas path at a location downstream of the compressor and upstream of a combustion chamber of the combustor, the air outlet connected to the turbine for cooling in the turbine using air from the compressor conveyed through the turbine cooling air path; and wherein the turbine cooling air conduit is defined in part by an air conduit of a heat exchanger, the heat exchanger having a fluid conduit in fluid isolation from the air conduit and in thermal communication with the air conduit, the fluid conduit extending from a hydrogen inlet of the fluid conduit to a hydrogen outlet of the fluid conduit, the hydrogen inlet being fluidly connected to a source of hydrogen, the hydrogen outlet being fluidly connected to the combustor, characterized in that: the heat exchanger is a downstream heat exchanger and the primary gas path is defined in part by an air conduit of an upstream heat exchanger at a location in the primary gas path that is between adjacent compressor stages of the plurality of compressor stages (140, 142), the upstream heat exchanger having a fluid conduit in fluid isolation from the air conduit of the upstream heat exchanger and in thermal communication with the air conduit of the upstream heat exchanger; the fluid conduit of the downstream heat exchanger is fluidly connected to the source of hydrogen via the fluid conduit of the upstream heat exchanger; the combustor is fluidly connected to the source of hydrogen via a hydrogen conduit defined in part by the fluid conduits (128, 328) of the upstream and downstream heat exchangers (122, 322) and by a pump operable to move hydrogen from the source of hydrogen to the combustor; and the hydrogen conduit is defined in part by a gaseous hydrogen accumulator at a location in the hydrogen conduit that is fluidly downstream of the fluid conduits (128, 328) of the upstream and downstream heat exchangers (122, 322). a primary gas path having, in fluid series communication: a primary air inlet, a compressor fluidly connected to the primary air inlet, a combustor fluidly connected to an outlet of the compressor, and a turbine fluidly connected to an outlet of the combustor, the turbine operatively connected to the compressor to drive the compressor; and a turbine cooling air conduit extending from an air inlet of the turbine cooling air conduit to an air outlet of the turbine cooling air conduit, the upstream air inlet connected in fluid communication with the primary gas path at a location downstream of the compressor and upstream of a combustion chamber of the combustor, the air outlet connected to the turbine for cooling in the turbine using air from the compressor conveyed through the turbine cooling air path; and wherein the turbine cooling air conduit is defined in part by an air conduit of a heat exchanger, the heat exchanger having a fluid conduit in fluid isolation from the air conduit and in thermal communication with the air conduit, the fluid conduit extending from a hydrogen inlet of the fluid conduit to a hydrogen outlet of the fluid conduit, the hydrogen inlet being fluidly connected to a source of hydrogen, the hydrogen outlet being fluidly connected to the combustor, the heat exchanger is a downstream heat exchanger and the primary gas path is defined in part by an air conduit of an upstream heat exchanger at a location in the primary gas path that is between adjacent compressor stages of the plurality of compressor stages (140, 142), the upstream heat exchanger having a fluid conduit in fluid isolation from the air conduit of the upstream heat exchanger and in thermal communication with the air conduit of the upstream heat exchanger; the fluid conduit of the downstream heat exchanger is fluidly connected to the source of hydrogen via the fluid conduit of the upstream heat exchanger; the combustor is fluidly connected to the source of hydrogen via a hydrogen conduit defined in part by the fluid conduits (128, 328) of the upstream and downstream heat exchangers (122, 322) and by a pump operable to move hydrogen from the source of hydrogen to the combustor; and the hydrogen conduit is defined in part by a gaseous hydrogen accumulator at a location in the hydrogen conduit that is fluidly downstream of the fluid conduits (128, 328) of the upstream and downstream heat exchangers (122, 322).