[en] Diphoton radiation of strongly interacting matter resulting from ultrarelativistic heavy-ion collisions is estimated for SPS and RHIC conditions. At SPS energies the thermal diphoton signal competes strongly with the Drell-Yan like background. For given charged-particle rapidity density a scenario with deconfinement transition predicts a larger diphoton yield than a scenario without phase transition. For RHIC energies we find that radiation from initially undersaturated (but gluon-rich) deconfined matter overwhelms the hadron gas and the Drell-Yan like diphotons in the invariant mass window 1< M<2.5 GeV. Due to this the so-called M _{perpendicularto} scaling is approximately obtained and can serve as additional tool for discriminating radiation from quark-gluon matter. (orig.)