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A subgroup $H$ of a group $G$ is called {\it pronormal}, if for every $g\inG$ subgroups $H$ and $H^g$ are conjugate in $\langle H, H^g\rangle$. It isproven that if a finite group $G$ possesses a $\pi$-Hall subgroup for a set ofprimes $\pi$, the every its normal subgroup (in particular, $G$ itself)possesses a $\pi$-Hall subgroup that is pronormal in~$G$.

The existence of pronormal $\pi$-Hall subgroups in $E_\pi$-groups