  We prove that for every integer $r\geq 2$, an $n$-vertex $k$-uniform
hypergraph $H$ containing no $r$-regular subgraphs has at most
$(1+o(1)){{n-1}\choose{k-1}}$ edges if $k\geq r+1$ and $n$ is sufficiently
large. Moreover, if $r\in\{3,4\}$, $r\mid k$ and $k,n$ are both sufficiently
large, then the maximum number of edges in an $n$-vertex $k$-uniform hypergraph
containing no $r$-regular subgraphs is exactly ${{n-1} \choose {k-1}}$, with
equality only if all edges contain a specific vertex $v$. We also ask some
related questions.
