  Let $k$ be a positive integer. Let $G$ be a balanced bipartite graph of order
$2n$ with bipartition $(X, Y)$, and $S$ a subset of $X$. Suppose that every
pair of nonadjacent vertices $(x,y)$ with $x\in S, y\in Y$ satisfies
$d(x)+d(y)\geq n+1$. We show that if $|S|\geq 2k+2$, then $G$ contains $k$
disjoint cycles covering $S$ such that each of the $k$ cycles contains at least
two vertices of $S$. Here, both the degree condition and the lower bound of
$|S|$ are best possible. And we also show that if $|S|=2k+1$, then $G$ contains
$k$ disjoint cycles such that each of the $k$ cycles contains at least two
vertices of $S$.
