We study integral 2-commodity flows in networks with a
special characteristic, namely symmetry. We show that the Symmetric
2-Commodity Flow Problem is in $P$, by proving that the cut criterion
is a necessary and sufficient condition for the existence of a
solution. We also give a polynomial-time algorithm whose complexity is
\textbf{$6C_{flow}+O(|A|)$}, where $C_{flow}$ is the time complexity
of your favorite flow algorithm (usually in $O(|V|\times|A|)$). Our
result closes an open question in a surprising way, since it is known
that the Integral 2-Commodity Flow Problem is NP-complete for both
directed and undirected graphs. This work finds application in optical
telecommunication networks.