Excited band structures recently observed in 156 Dy are investigated using the microscopic triaxial projected shell model (TPSM) approach and the quasiparticle random phase approximation (QRPA) based on the rotating mean-field. It is demonstrated that new observed excited bands, tracking the ground-state band, are the γ-bands based on the excited two-quasineutron configurations as conjuctured in the experimental work.