The compressor and turbine plenums (7,10) are connected by an annular space (13) which is enclosed in a double-wall housing (12) which is used to blow the cooling air from compressor to turbine plenums within the gas turbine. Alternatively tubes which are held close to the housing wall may be used, or channels that may be enclosed within the housing (12) forming the connection and being assisted by an intermediate cooler arranged between the two plenums. The annulus is formed by the double wall structure of the housing and forms part of the connection between compressor and turbine chambers. Part of the cooling air may also be directed to the combustion chamber (50). The intermediate cooler may be arranged within the specified annulus and may use water to cool down the passing air, serving as the connection between the two plenums.