This paper develops a formalism of variation of Hodge-Tate structures. The theory of Hodge-Tate structure was introduced by Tate as a p-adic analogue of classical Hodge theory. Faltings has found the so-called Hodge-Tate decomposition, which may be considered as a p-adic counterpart of classical Hodge decomposition concerning the cohomology group of the constant sheaf. To generalize this to the cohomology groups of local systems, the notion ``Hodge-Tate'' is introduced for a smooth \({\mathbb{Q}}_ p\)-sheaf on a smooth variety over a p-adic field. Then a result concerning stability is obtained. Namely, it is shown that the higher direct image of a Hodge-Tate sheaf by a proper smooth morphism is still a Hodge-Tate sheaf.