Rotational structures have been measured using the Jurogam II and GAMMASPHERE arrays at low spin following the 155 Gd(α,2n) 157 Dy and 148 Nd( 12 C, 5n) 155 Dy reactions at 25 and 65 MeV, respectively. We report high-K bands, which are conjectured to be the first candidates of a K π = 2 + γ vibrational band, built on the [505]11/2neutron orbital, in both odd-A 155, 157 Dy isotopes. The coupling of the first excited K=0 + states or the so-called β vibrational bands at 661 and 676 keV in 154 Dy and 156 Dy to the [505]11/2orbital, to produce a K π =11/2band, was not observed in both 155 Dy and 157 Dy, respectively. The implication of these findings on the interpretation of the first excited 0 + states in the core nuclei 154 Dy and 156 Dy are also discussed.