  In a graph $G$, let $\mu_G(xy)$ denote the number of edges between $x$ and
$y$ in $G$. Let $\lambda K_{v,u}$ be the graph $(V\cup U,E)$ with $|V|=v$,
$|U|=u$, and \[ \mu_G(xy)=\begin{cases} \lambda &\mbox{if $x\in U$ and $y\in V$
or if $x\in V$ and $y\in U$}\\ 0 &\mbox{otherwise.} \\ \end{cases} \] Let $M$
be a sequence of non-negative integers $m_1,m_2,\ldots,m_n$. An $(M)$-cycle
decomposition of a graph $G$ is a partition of the edge set into cycles of
lengths $m_1,m_2,\ldots,m_n$. In this paper, we establish necessary and
sufficient conditions for the existence of an $(M)$-cycle decomposition of
$\lambda K_{v,u}$.
