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The possibilities of construction superconducting synchrotron magnets with pulse repetition rate up to 20 Hz are analyzed. Different design concepts are considered. The expected AC power losses and the magnet cooling conditions are calculated based on the data which have been obtained under design, construction and long term tests of 2 T superferric dipoles of the Nuclotron at the frequencies up to f=2 Hz. New experimental data on the investigation of the dipole at higher frequencies are presented. Hollow multifilament NbTi composite cable cooled with two-phase helium flow is used. The essential features of the test bench are described.