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High-resolution, inelastic x-ray scattering measurements of the dynamic structure factor S(Q, ω) of liquid water have been performed for wave vectors Q between 4 and 30 nm −1 in distinctly different thermodynamic conditions (T= 263 -420 K ; at, or close to, ambient pressure and at P = 2 kbar). In agreement with previous inelastic x-ray and neutron studies, the presence of two inelastic contributions (one dispersing with Q and the other almost non-dispersive) is confirmed.The study of their temperature-and Q-dependence provides strong support for a dynamics of liquid water controlled by the structural relaxation process. A viscoelastic analysis of the Q-dispersing mode, associated with the longitudinal dynamics, reveals that the sound velocity undergoes the complete transition from the adiabatic sound velocity (c 0 ) (viscous limit) to the infinite frequency sound velocity (c ∞ ) (elastic limit). On decreasing Q, as the transition regime is approached from the elastic side, we observe a decrease of the intensity of the second, weakly dispersing feature, which completely disappears when the viscous regime is reached. These findings unambiguously identify the second excitation to be a signature of the transverse dynamics with a longitudinal symmetry component, which becomes visible in the S(Q, ω) as soon as the purely viscous regime is left.