Abstract: The magnetic dipole moments (mu) of Tl-209(g)(N =128) and Tl-207(m)(N = 126) have been measured for the first time using the in -source laser resonance -ionization spectroscopy technique with the Laser Ion Source and Trap (LIST) at ISOLDE (CERN). The application of the LIST suppresses the usually overwhelming background of the isobaric francium isotopes and allows access to heavy thallium isotopes with >207. The self -consistent theory of finite Fermi systems based on the energy density functional by Fayans et al. well describes the N dependence of μfor 1/2(+) thallium ground states, as well as μfor the 11/2(-) isomeric states in europium, gold and thallium isotopes. The inclusion of particle-vibration coupling leads to a better agreement between the theory and experiment for mu(Tl-g , I-pi = 1/2(+)). It is shown that beyond mean-field contributions tocannot be neglected at least for thallium isotopes with I-pi = 1/2(+).