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We analysed our experimental recent findings of the dipole response of the odd-mass stable nucleus 205Tl within the quasi-particle phonon model. Using the phonon basis constructed for the neighbouring 204Hg and wave function configurations for 205Tl consisting of a mixture of quasiparticle ⊗ N-phonon configurations (N=0,1,2), only one group of fragmented dipole excited states has been reproduced at 5.5 MeV in comparison to the experimental distribution which shows a second group at about 5 MeV. The computed dipole transition strengths are mainly of E1 character which could be associated to the pygmy dipole resonance.