The effects of the Dzyaloshinskii-Moriya (DM) and the Kaplan-Shekhtman-Entinwohlman-Aharony (KSEA)superexchange interactions on the ground state properties of the one-dimensional spin-Peilers system in open chain are studied by using the Lanczos numerical method. The study concentrates mainly on the influence of systemic dimerisation in open chain. The results show that systemic ground state energy density varies with dimerisation parameter δ in different DM interactions, and there exists a special point δc> where the DM interaction has no influence on the systemic dimerisation, no matter whether the DM interaction is relative or irrelative to systemic dimerisation (η = 1 or η= 0). The KSEA interaction has no fixed special point, but the points of intersection are dense relatively in a certain numberical value range, and sparse in other numberical value ranges. So we can conclude that the antisymmetric anisotropy DM interaction differs from the symmetric anisotropy KSEA interaction, but they are analogous in the sense of the influence of systemic dimerisation in open chain.