A rotary storage heat exchanger structure for multi-shaft gas turbines, especially motor vehicle gas turbines. The same is arranged in a housing and is provided with one or more rotatable disc-shaped storage bodies having flow passages which extend substantially parallel to the axis of rotation of the storage body or bodies. There are hot exhaust gases and colder compressed working air passed through the passages. The storage body or each of the storage bodies is journaled in a housing web in an overhung position or is journaled at two bearing areas in a housing web or in a housing web and another structural part of the gas turbine. In spaced relationship to the storage body, nozzle gap means are provided on or in the housing in the extended plane separating the working air flow and exhaust gas flow play is provided between the storage body and the pertaining housing web and the inner working air and exhaust gas flow conducting devices.