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The discovery of the triaxial superdeformed bands provide a new opportunity to understand the axial symmetry breaking even in highly elongated nuclei. A total of 17 triaxial superdeformed nuclei in the mass A ~ 160 region and 11 in the mass A ~ 80 region are predicted by the three dimensional total routhian surface calculations. A possible way to identify the triaxiality of triaxial superdeformed nuclei is suggested.