  Using the technique of amalgamation-detachment, we show that the complete
equipartite multigraph $\lambda K_{n\times m}$ can be decomposed into cycles of
lengths $c_1m,\dots,c_km$ (plus a 1-factor if the degree is odd) whenever there
exists a decomposition of $\lambda m K_n$ into cycles of lengths $c_1,
\dots,c_k$ (plus a 1-factor if the degree is odd). In addition, we give
sufficient conditions for the existence of some other, related cycle
decompositions of the complete equipartite multigraph $\lambda K_{n\times m}$.
