The electric efficiencies of existing back-pressure power stations can be increased noticeably by blowing the exhaust steam of the back-pressure turbine into the combustion chamber of a following gas turbine. The steam will be resuperheated in the high-temperature range. As the steam will be used simultaneously for cooling the combustion chamber, it is possible to work without cooling air and reduce the compressor performance noticeably. The exhaust heat of the gas turbine can be used in a waste heat boiler for further steam generation required for the blowing into the combustion chamber. The use of a two-pressure boiler makes it possible to expand the HP-steam in a following back-pressure steam turbine to the pressure in the combustion chamber, ahead of blowing it into the combustion chamber. This leads to a further increase in efficiency. The high steam part in the waste gas, due to the process, enables the extraction of a considerable amount of district heat with the aid of a flue gas condenser. The available temperature level corresponds to that of a heating condenser in a conventional steam power plant. In the case of retrofitting, the chosen configuration allows to operate the existing plant practically undisturbed. The uncoupling of parts on the firing side makes it possible to use the present fuel in the existing part of the plant without restrictions.