[en] We report on inelastic neutron scattering experiments carried out on single-crystals of the YBa₂Cu₃O_6+x system. The spin dynamics has been systematically investigated in the six typical regimes: the pure and doped AF states (x = 0.15, 0.37), the weakly doped (x = 0.45, 0.51), the heavily doped (x = 0.69, 0.92) and the overdoped (x = 1) metallic states which all exhibit a superconducting ground state. The hole doping strongly affects the AF-order, dynamical QF-correlations remain in the metallic state. An energy gap has been discovered in the spin excitation spectrum of any superconducting samples, however, it becomes weaker close to the I-M transition. A quite unusual T-dependence of the spin excitation spectrum was found. (author). 22 refs., 18 figs