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In each Menger manifold $M$ we construct: (i) a closed nowhere dense subset$M_0$ which is homeomorphic to $M$ and is universal nowhere dense in the sensethat for each nowhere dense set $A\subset M$ there is a homeomorphism $h$ of$M$ such that $h(A)\subset M_0$; (ii) a meager $F_\sigma$-set $\Sigma_0\subsetM$ which is universal meager in the sense that for each meager subset $B\subsetM$ there is a homeomorphism $h$ of $M$ such that $h(B)\subset \Sigma_0$.  Also we prove that any two universal meager $F_\sigma$-sets in $M$ areambiently homeomorphic.

Universal nowhere dense and meager sets in Menger manifolds