The level schemes of the deformed odd-proton nuclei 171Lu and 173Lu have been studied by in-beam spectroscopy. Measurements of singles γ-ray spectra, angular distributions and γ-γ coincidences were performed in the 169Tm(α, 2nγ) 171Lu reaction at 27 MeV α-particle energy. In the reaction 173Yb(d, 2nγ) 173Lu singles spectra and γ-γ coincidences were measured. Additional γ-ray spectra were taken for the reactions 169Tm(α, 2nγ) 171Lu at E α = 23 MeV and 173Yb(p, nγ) 173Lu. The proposed level schemes of 171Lu and 173Lu involve rotational bands of the intrinsic states 7 2 +[404] , 1 2 +[411] , 5 2 +[402] , 1 2 −[541] and 9 2 −[514] up to spin 25 2 , 23 2 , 23 2 , 29 2 and 21 2 , respectively, in 171Lu and up to spin 23 2 , 17 2 , 19 2 , 25 2 , and 23 2 , respectively, in 173Lu. Transitions between some states of the 1 2 +[411] and 5 2 +[402] bands in 171Lu indicate a strong mixing of states with ΔK = 2. Similarly, a ΔK = 4 mixing between states of the 1 2 −[541] and 9 2 −[514] bands in 171Lu is indicated by interband transitions. These mixings are described in terms of the rotation-particle coupling, considering only the interaction between states with K and K±1. The dependence of the side feeding to the 1 2 −[541] and 7 2 +[404] bands on the level spins and energies was investigated.