In this paper, we will investigate joint upper and lower semi-continuity of two-variable set-valued functions. More precisely. among other results, we will show that under certain conditions, a two-variable lower horizontally quasi-continuous mapping $F:X \\times Y \\to \\mathcal{K}(Z)$ is jointly upper semi-continuous on sets of the from $D \\times \\{y_0\\}$, where $D$ is a dense $G_\\delta$ subset of $X$ and $y_0 \\in Y$. Similar result for joint lower semi-continuity of upper horizontally quasi-continuous mappings is obtained. These will improve some known results on joint continuity of single-valued functions.

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