  Let $k_r(n,\delta)$ be the minimum number of $r$-cliques in graphs with $n$
vertices and minimum degree $\delta$. We evaluate $k_r(n,\delta)$ for $\delta
\leq 4n/5$ and some other cases. Moreover, we give a construction, which we
conjecture to give all extremal graphs (subject to certain conditions on $n$,
$\delta$ and $r$).
