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We obtain a strong generalisation of the classic Hilton-Milner theorem on cross intersecting families. In particular, we determine the maximum of $\\sum_{j\\in [r]}\\vert\\mathcal{F}_j\\vert$ for $r$-cross $t$-intersecting families in the cases when these are $k$-uniform families or arbitrary subfamilies of $\\mathscr{P}([n])$. 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