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We establish a Hörmander type theorem for the multilinear pseudo-differential operators, which is also a generalization of the results in \cite{MR4322619} to symbols depending on the spatial variable. Most known results for multilinear pseudo-differential operators were obtained by assuming their symbols satisfy pointwise derivative estimates(Mihlin-type condition), that is, their symbols belong to some symbol classes $n$-$\mathcal{S}^m_{ρ, δ}(\mathbb{R}^d)$, $0 \le δ\le ρ\le1$, $0 \le δ