In this article, we review our recent neutron diffraction and quasielastic scattering works on the following three water systems related to the formation of clathrate hydrates. The first is aqueous solutions of organic guest molecules. The second is the aqueous solutions prepared by applying high pressure of non-polar guest gas molecules. The third is the amorphous solids prepared by depositing mixed gases of water and guest molecules on a cold substrate (10 K). In the first system, the diffusion coefficient of water molecules was smaller than that in bulk water and it depended on the size of guest molecules. In the second system, the diffusion of water molecules became excessively slower below the formation temperature of gas hydrates and it depended on the amounts of solved guest molecules and formed hydrate crystals. In the third system, as the temperature of the amorphous solids increased, the local cage structure grew up above the glass transition temperature (ca. 130 K) and finally hydrate crystals formed at 165 K. All of the above results indicate that the local structural fluctuation of hydrate cage occurs in the liquid or amorphous states in advance of the crystallization of clathrate hydrates.