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The study of superferric synchrotron magnets with a pulse repetition rate up to 20 Hz is performed at the Laboratory of High Energies of the JINR during the last years. The magnet feature is a low inductance superconducting coil made of a high current hollow cable, cooled with two-phase helium flow at 4.5 K. After the successful tests of fast-cycling 1.4 m model dipoles at the field ramp up to 7 T/s, a proper quadrupole is under design and construction. The new magnet yoke length is about 420 mm and the distance between the pole shoes is 90 mm. The cable comprises 24 wires of 0.73 mm diameter are wound around a copper-nickel tube with an outer diameter of 5 mm. The wire consists of 10374 NbTi filaments of 4.2 mum diameter. It is expected that the new 32 T/m quadrupole magnet will operate at pulse repetition rate up to 10 Hz providing the field gradient ramp of 600 T/m per second. The first tests have been carried out in August 2006. Status of the work and obtained results are presented and discussed.