Although the systematics of the Pygmy Dipole Resonance was established in several stable even–even nuclei, the collectivity of this mode, explained in a macroscopic picture as an oscillation of a neutron skin against an isospin symmetric proton–neutron core, is still not well understood. In order to guide the theoretical models, we investigated the heavy odd mass, stable isotopes 203,205Tl using unpolarized bremsstrahlung photon beams at the S-DALINAC facility at TU Darmstadt. The NRF experiments were complemented by measurements at the High Intensity γ-ray Source (HIγS) at the Triangle Universities Nuclear Laboratory (TUNL) in Durham, NC, USA, with a fully linearly polarized quasi-monoenergetic photon beam. Between 4 and 7 MeV, a concentration of dipole strength is observed in the odd-mass nuclide 205Tl. For the 203Tl isotope, two ground-state transitions around 5 MeV could be resolved in the spectra. In this report, the obtained results will be presented. The results for the proton-odd nuclide 205Tl will be compared to the ones for the neighbouring even–even nucleus 206Pb.