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It was recently found that the addition of special elements leading to the deviation from the three empirical rules for the achievement of high glass-forming ability causes new mixed structures consisting of the amorphous phase containing nanoscale compound or quasicrystal particles in Zr–Al–Ni–Cu–M (M=Ag, Pd, Au, Pt or Nb) bulk alloys prepared by the copper mold casting and squeeze casting methods. In addition, the mechanical strength and ductility of the nonequilibrium phase bulk alloys are significantly improved by the formation of the nanostructures as compared with the corresponding amorphous single phase alloys. The composition ranges, formation factors, preparation processes, unique microstructures and improved mechanical properties of the nanocrystalline and nanoquasicrystalline Zr-based bulk alloys are reviewed on the basis of our recent results reported over the last two years. The success of synthesizing the novel nonequilibrium, high-strength bulk alloys with good mechanical properties is significant for the future progress of basic science and engineering.