In this paper, we study a relative two-weight $\mathbb{Z}_2 \mathbb{Z}_4$-additive codes. It is shown that the Gray image of a two-distance $\mathbb{Z}_2 \mathbb{Z}_4$-additive code is a binary two-distance code and that the Gray image of a relative two-weight $\mathbb{Z}_2 \mathbb{Z}_4$-additive code, with nontrivial binary part, is a linear binary relative two-weight code. The structure of relative two-weight $\mathbb{Z}_2 \mathbb{Z}_4$-additive codes are described. Finally, we discussed permutation automorphism group of a $\mathbb{Z}_2 \mathbb{Z}_4$-additive codes.

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