In this paper, we study the kth stability of spacelike hypersurfaces in the Lorentz space L^{n+1}. The stability of order k (briefly, k-stability) is a natural extension of the ordinary stability. The k-stability is de ned based on the linearized operator L_k as an extension of the Laplace operator (i.e. L_0 = ). We give suffcient conditions for a bounded domain in a k-maximal hypersurface of the Lorentz-Minkowski space to be k-stable. Especially, in the case k = 1, the Gauss- Kronecker curvature of 1-stable hypersurfaces has to be null on a special submanifold.
