Abstract.  

The aim of this paper is to study the properties of the nilradical of Lie triple algebras as a generalization of the nilradical of Lie triple systems studied par Nora C.Hopkins . At first, we study the nilpo- tent ideals in Lie triple algebras and we show that an ideal H of a Lie triple algebra T is T-nilpotent if and only if the ideal H + D(T;H) generated by H is a nilpotent ideal of the standard envelopping Lie algebra T +D(T; T) of T: Afterwards, the existence of the nilradical of Lie triple algebras is shown and a relationship between the nilradical of a Lie triple algebra, the one of its standard envelopping Lie algebra and that of an ideal is established.