Abstract: It is studied that the representation of the Lie algebras in the Yetter-Drinfel’d category HH YD(i.e. generalized H-Lie algebras). The Engel’s theorem for generalized H-Lie algebras is proved: Let L be a generalized H-Lie algebra, if every cyclic Yetter-Drinfel’d submodule of L is ad-nilpotent, then L is nilpotent.

Key words: Generalized H-Lie algebra, Engel’s theorem, Yetter-Drinfel’d category