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The strongly coupled phase of the quark-gluon plasma (QGP) is studied here by resorting to a T-matrix formulation in which the medium is seen as a nonideal gas of quasiparticles (quarks, antiquarks, and gluons) interacting nonpertubatively. In the temperature range under study, (1-5)Tc, where Tc is the temperature of deconfinement, the interactions are expected to be strong enough to generate bound states. The dissociation temperature of such binary bound states is thus computed here. The more the quasiparticles involved in the binary system are heavy, the more the bound state is likely to survive significantly above Tc. Then the QGP equations of state at zero and small baryonic potential are computed for Nf = 2 and Nf = 2 + 1 by resorting to the Dashen, Ma, and Bernstein formulation of statistical mechanics. Comparisons with current lattice QCD data are presented. [ABSTRACT FROM AUTHOR]