A recuperative exhaust-gas heat exchanger for a gas turbine engine is provided which has a crossflow/counterflow matrix around which the hot turbine exhaust gas flows, a distributing tube for directing the air delivered by a compressor into the crossflow/counterflow matrix and a collecting tube which is arranged parallel to the distributing tube and is intended for discharging the compressor air, heated via the crossflow/counterflow matrix, to a consumer. End faces of the distributing and collecting tubes which are remote from the compressor and consumer are closed. The closed end face of the collecting tube is firmly connected axially and radially to the turbine casing.