The strongly coupled phase of Yang-Mills plasma with arbitrary gauge group is studied in a T matrix approach. The existence of lowest-lying glueballs, interpreted as bound states of two transverse gluons (quasiparticles in a many-body setup), is analyzed in a nonperturbative scattering formalism with the input of lattice-QCD static potentials. Glueballs are actually found to be bound up to 1.3 T c . Starting from the T-matrix, the plasma equation of state is computed by resorting to a formulation of statistical mechanics (Dashen et al.) and favorably compared to quenched lattice data. Special emphasis is put on SUðNÞ gauge groups, for which analytical results can be obtained in the large-N limit, and predictions for a G 2 gauge group are also given in this work.