  Let $D=(V,A)$ be a directed graph of order $n\geq 6$. Let $W$ be a subset of
$V$ with $|W|\geq 6$. Suppose that every vertex of $W$ has degree at least
$(3n-3)/2$ in $D$. Then for any integer partition $|W|=n_1+n_2$ with $n_1\geq
3$ and $n_2\geq 3$, $D$ contains two disjoint directed cycles $C_1$ and $C_2$
such that $|V(C_1)\cap W|=n_1$ and $|V(C_2)\cap W|=n_2$. We conjecture that for
any integer partition $|W|=n_1+n_2+\cdots +n_k$ with $k\geq 3$ and $n_i\geq
3(1\leq i\leq k)$, $D$ contains $k$ disjoint directed cycles $C_1,C_2,\ldots ,
C_k$ such that $|V(C_i)\cap W|=n_i$ for all $1\leq i\leq k$. The degree
condition is sharp in general.
