We report dielectric relaxation studies of aqueous solutions of two water-like molecules, hydrazine and hydrogen peroxide, in the neighborhood of their glass transition temperatures, T-g. These solutions behave in a rather simple manner, reminiscent of the diols and diamines of which they are the limiting cases. Their relaxations near Tg are more nearly exponential than in most other cases, and they show essentially no secondary relaxations. Supercooled hydrazine solutions are the more stable. At the composition 20 mol % N2H4, the liquid exhibits precise time-temperature-superposition (TTS) behavior. At higher N2H4 contents, a weak deviation from TTS appears. The temperature dependence of the relaxation time follows the Vogel-Fulcher-Tammann (VFT) equation, and the strength parameter, D, is similar to that of glycerol, a liquid of intermediate fragility. The VFT divergence temperature, To, lies close to the Kauzmann temperature, T-K, determined earlier from calorimetric studies implying that the thermodynamic and kinetic measures of fragility are very similar. Tg values assessed from T(tau=100s) agree well with observed calorimetric, T-g's. Extrapolation of the relaxation time behavior to pure water would imply a Tg for water of 135-140 K; however, the dielectric behavior of amorphous solid water in the temperature range 130-160 K is completely different from that of the solutions showing no sign of the loss peak exhibited by all the solutions. Based on the solution behavior, water controversially must either remain glassy up until the temperature of crystallization or be an almost ideally strong liquid above 136 K. Having shown elsewhere how this implies glassy character up to LDA crystallization and a Tg above 160 K, we now examine the implications for water structure reorganization on dissolution of solutes, certain glycols excepted. It appears that the water in these solutions behaves like ice III rather than ice I.