  A congruence $\varepsilon$ on a semigroup $S$ is perfect if for any
congruence classes $x\varepsilon$ and $y\varepsilon$ their product as subsets
of $S$ coincides (as a set) with the congruence class $(xy)\varepsilon$.
Perfect congruences on the bicyclic semigroup were found in \cite{key7}. Using
the structure of bisimple $\omega$-semigroups determined in \cite{key25} and
the description of congruences on these semigroups found in \cite{key20} and
\cite{key1}, we obtain a complete characterization of perfect congruences on
all bisimple $\omega$-semigroups, substantially generalizing the above
mentioned result of \cite{key7}.
