Popularized by Becke at the beginning of the nineties, the global-hybrid (GH) approximation has largely contributed to the wide enthusiasm of chemists for DFT and later for TDDFT. By partially canceling the one-electron SIE and its extension of many-electron systems, it systematically improves the performance of semilocal approximations in modeling ground-state energy-and density-based properties. Its excellent performance are also recognized at excited state. For instance, it is considered as part of the state-of-the-art when applied to the modeling of 'local' valence exitation of organic chromophores. The GH exchange-correlation energy derives directly from the adiabatic-connection formalism in DFT. It mixes a fraction a x of nonlocal exact-like exchange (EXX) E EXX