© 2018, Korean Society for Computational and Applied Mathematics. In this paper we study Z 2 Z 4 Z 8 -additive codes, which are extensions of recently introduced Z 2 Z 4 -additive codes. We determine the standard forms of the generator and parity-check matrices of Z 2 Z 4 Z 8 -additive codes. Moreover, we investigate Z 2 Z 4 Z 8 -cyclic codes and give their generator polynomials and spanning sets. We also give some illustrative examples of both Z 2 Z 4 Z 8 -additive codes and Z 2 Z 4 Z 8 -cyclic codes.