Up to now, only one synchrotron (Nuclotron at JINR, Dubna) is equipped with fast-pulsed superconducting magnets. The demand for high beam intensities leads to the requirement of fast-pulsed magnets for synchrotrons. An example is the proposed international 'Facility for Antiproton and Ion Research' (FAIR) at GSI, which will consist of two synchrotrons in one tunnel, and several storage rings. The high field ramp rate and repetition frequency introduce many magnet design problems and constraints on the operation of the accelerator. Persistent currents in the superconductor and eddy currents in wire, cable, iron and vacuum chamber reduce the field quality and generate cryogenic losses. Due to the large number of magnet cycles during the lifetime of such a magnet, special attention has to be paid to magnet structure and material fatigue problems. The large charging voltages put some constraints on the use of cold diodes for quench protection.R&D has started at GSI, in collaboration with many institutions, to comply with the constraints mentioned above. Model dipoles were built and tested. The results of the R&D are reported. The advantages of the use of low field,fast-pulsed superconducting, (as opposed to resistive), magnets will be discussed.