  This paper is devoted to a detailed study of nowhere-zero flows on signed
eulerian graphs. We generalise the well-known fact about the existence of
nowhere-zero $2$-flows in eulerian graphs by proving that every signed eulerian
graph that admits an integer nowhere-zero flow has a nowhere-zero $4$-flow. We
also characterise signed eulerian graphs with flow number $2$, $3$, and $4$, as
well as those that do not have an integer nowhere-zero flow. Finally, we
discuss the existence of nowhere-zero $A$-flows on signed eulerian graphs for
an arbitrary abelian group~$A$.

Combinatorics