Abstract: 2-Harmonic spacelike submanifolds in a pseudoRiemannian space form was studied, and a Simons form inequality of integration was obtained via calculations. After the submanifold was restricted it became a maximal spacelike submanifold, and the Simons form integral inequality was used to discuss the submanifold properties when the sectional curvature of the pseudoRiemannian space form is positive, negative and zero, respectively, and some results were obtained.

Key words: 2-harmonic, totally geodesic, spacelike submanifold