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In this paper, we will determine the upper bound of $|\\mathcal A||\\mathcal B|$ for cross-$2$-intersecting families $\\mathcal A\\subseteq\\binom{[n]}{k}$ and $\\mathcal B\\subseteq\\binom{[n]}{\\ell}$. The structures of the extremal families attaining the upper bound are also characterized. 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Let $n$, $k$ and $\\ell$ be positive integers such that $n\\geq 3.38\\ell$ and $\\ell\\geq k\\geq 2$. In this paper, we will determine the upper bound of $|\\mathcal A||\\mathcal B|$ for cross-$2$-intersecting families $\\mathcal A\\subseteq\\binom{[n]}{k}$ and $\\mathcal B\\subseteq\\binom{[n]}{\\ell}$. The structures of the extremal families attaining the upper bound are also characterized. 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