  An indecomposable flow $f$ on a signed graph $\Sigma$ is a nontrivial
integral flow that cannot be decomposed into $f=f_1+f_2$, where $f_1,f_2$ are
nontrivial integral flows having the same sign (both $\geq 0$ or both $\leq 0$)
at each edge of $\Sigma$. This paper is to classify indecomposable flows into
characteristic vectors of circuits and Eulerian cycle-trees --- a class of
signed graphs having a kind of tree structure in which all cycles can be viewed
as vertices of a tree. Moreover, each indecomposable flow other than circuit
characteristic vectors can be further decomposed into a sum of certain half
circuit characteristic vectors having the same sign at each edge. The variety
of indecomposable flows of signed graphs is much richer than that of ordinary
unsigned graphs.
