Based on interaction potentials between a heavy quark and antiquark as extracted from recent unquenched QCD lattice calculations we calculate $T$-matrix and quark selfenery in the color-singlet and -octet channels in the temperature range 1-2 T_c. We find that quasiparticle have a masses of around 200~MeV, and a width comparable to their mass. These results strongly support the idea that in this range of temperatures the QGP behaves as a strongly interacting liquid rather than a gas. Moreover we find that the attractive color-singlet part of the interaction results in a $q$-$\bar q$ $T$-matrix with both bound-state and resonant-like structures for T \le 2 T_c.