Rotational structures have been measured using the Jurogam II and GAMMASPHERE arrays at low spin following the Gd155(α,2n)Dy157 and Nd148(C12,5n)Dy155 reactions at 25 and 65 MeV, respectively. We report high-K bands, which are conjectured to be the first candidates of a Kπ=2+γ vibrational band, built on the [505]11/2- neutron orbital, in both odd-ADy155,157 isotopes. The coupling of the first excited K=0+ states or the so-called β vibrational bands at 661 and 676 keV in Dy154 and Dy156 to the [505]11/2- orbital, to produce a Kπ=11/2- band, was not observed in both Dy155 and Dy157, respectively. The implication of these findings on the interpretation of the first excited 0+ states in the core nuclei Dy154 and Dy156 are also discussed.