本文在一般的Ｂａｎａｃｈ空间Ｘ中研究从非空闭集ＫＸ到Ｘ的非凸集值映射Ｆ的包含切性问题．得到的结果定理３．１把有关的结论推广到非光滑空间，定理３．３则将有限维空间的正则性定理推广到任意的Ｂａｎａｃｈ空间．作为结果的应用，我们证明了无穷维非凸微分包含和非凸控制系统生存解的存在性，且给出了一个方便的等价切性条件．

In this paper,we investigate the tangent properties of inclusion for the set-valued map F defined on K which is a closed subset of a Banach space X with nonempty and nonconvex values in X.Our results extend the results of [1,p.161] and [9, p.125].As the examples of application, two viability problems for nonconvex differential inclusions and nonconvex control systems in infinite dimensional spaces are considered.A convenient tangential condition which is equivalent to the tangential condition of[8]is also given.