[en] The doubly-odd nucleus ¹⁶⁴Tm was studied in the ¹⁵⁰Nd(¹⁹F,5n) reaction at 85 MeV. Γ-ray spectroscopic measurements with the NORDBALL detector system were performed. The proposed level scheme of ¹⁶⁴Tm consists of six new and three known but reinvestigated rotational bands, which are based on either the K^π = 6^- isomer of the K^π = 1⁺ ground state. Most of these bands show the common feature of a very small signature splitting (Δe' ∼ 0 at ℎω =0.15 MeV). Therefore, a discussion of the experimental results in the framework of the open-quotes Tilted Axis Crankingclose quotes model is suitable. This discussion will also contain comparisons with particle-rotor and open-quotes Principal Axis Crankingclose quotes model predictions