There is a plethora of experimental data on the dynamics of water in mixtures with glycerol, ethylene glycol, ethylene glycol oligomers, poly(ethylene glycol) 400 and 600, propanol, poly(vinyl pyrrolidone), poly(vinyl methylether), and other substances. In spite of the differences in the water contents, the chemical compositions, and the glass transition temperatures T-g of these aqueous mixtures, a faster relaxation originating from the water (called the nu-process) is omnipresent, sharing the following common properties. The relaxation time tau(nu) has Arrhenius temperature dependence at temperatures below T-g of the mixture. The activation energies of tau(nu) all fall within a neighborhood of 50 kJ/mol. At the same temperature where mixtures are all in their glassy states, the values of tau(nu) of several mixtures are comparable. The Arrhenius temperature dependence of tau(nu) does not continue to higher temperatures and instead it crosses over to a stronger temperature dependence at temperatures above T-g. The dielectric relaxation strength of the nu-process, Delta epsilon(nu)(T), has a stronger temperature dependence above T-g than below, mimicking the change of enthalpy, entropy, and volume when crossing T-g. These general property of the nu-process (except for the magnitude of the activation energy) had been found before in the secondary relaxation of the faster component in several binary nonaqueous mixtures. Other properties of the secondary relaxation in these nonaqueous mixtures have helped to identify it as the Johari-Goldstein (JG) secondary relaxation of the faster component. The similarities in properties lead us to conclude that the nu-processes in water mixtures are the JG secondary relaxations of water. The conclusion is reinforced by the processes behaving similarly to the nu-process found in 6 angstrom thick water layer (two molecular layers) in fully hydrated Na-vermiculite clay, and in water confined in molecular sieves, silica hydrogels, and poly(2-hydroxyethyl methacrylate) hydrogels.