In this paper, we investigate commuting dual truncated Toeplitz operators on the orthogonal complement of the model space $$K^{2}_{u}.$$ Let $$f,g \in L^{\infty },$$ if two dual truncated Toeplitz operators $$D_{f}$$ and $$D_{g}$$ commute, we obtain similar conditions of Brown–Halmos Theorem for Hardy-Toeplitz operators, that is, both *f* and *g* are analytic, or both *f* and *g* are co-analytic, or a nontrivial linear combination of *f* and *g* is constant. However, the first two conditions are not sufficient, one can easily construct two non-commuting dual truncated Toeplitz operators with analytic or co-analytic symbols. We prove that two bounded dual truncated Toeplitz operators $$D_{f}$$ and $$D_{g}$$ commute if and only if *f*, *g*, $${\bar{f}}(u-\lambda )$$ and $${\bar{g}}(u-\lambda )$$ all belong to $$H^{2}$$ for some constant $$\lambda ;$$ or $${\bar{f}},{\bar{g}}$$, $$f(u-\lambda )$$ and $$g(u-\lambda )$$ all belong to $$H^{2}$$ for some constant $$\lambda ;$$ or a nontrivial linear combination of *f* and *g* is constant.