  By analogy with the definition of group with triality we introduce Lie
algebra with triality as Lie algebra L wich admits the group of automorphisms
S_3={s,r | s^2=r^3=1, srs=r^2} such that for any x\in L we have
(x^s-x)+(x^s-x)^r+(x^s-x)^(r^2)=0. We describe the structure of finite
dimensional Lie algebra with triality over a field of characteristic 0 and give
applications of Lie algebras with triality to the theory of Malcev algebras.
