The magnetization and the differential magnetic susceptibility of DyxY3-xFe5O12 Single Crystals (x = 0.3; 0.62) have been measured in pulsed magnetic fields up to 50 T at temperatures below T 50 K. It was found that the total magnetic reversal of the rare-earth magnetic subsystem is realized through several jumps of the magnetic moment. The number of these jumps and their amplitudes depend on the orientation of the external field and on the composition of the crystals. A theoretical model for quantitative description of the observed phenomena was developed, within the framework of quasi-Ising ordering of rare earth ions.