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 similar to 160 r
egion and 11 in the mass A similar to 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.