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The Forschungszentrum Juelich (FZJ) has taken the leadership of a consortium to design and construct the HESR as part of the Facility for Antiproton an Ion Research (FAIR) project at the Gesellschaft fuer Schwerionenforschung (GSI) in Germany. The HESR is a 50 Tm synchrotron/storage ring for antiprotons using superconducting magnet technology, where the development of a bent dipole magnet (cosine theta) with a radius of curvature of 13.9 m and a length of 3.3 m is the major task. On basis of the HERA cooling system the cryogenic design for the HESR has started. One key issue will be the design of several cold-warm transitions e.g. at PANDA, the E-Cooler and in the region of the stochastic beam cooling system. Another important development is the cryostat layout housing the superconducting curved magnets and in particular the alignment system and measurement equipment for the bent magnets. This paper will present an overview both of the cryogenic layout and the cryostat design. It will give a status report on the achievements so far and discuss the future plans.