  We generalise to signed graphs a classical result of Tutte [Canad. J. Math. 8
(1956), 13--28] stating that every integer flow can be expressed as a sum of
characteristic flows of circuits. In our generalisation, the r\^ole of circuits
is taken over by signed circuits of a signed graph which occur in two types --
either balanced circuits or pairs of disjoint unbalanced circuits connected
with a path intersecting them only at its ends. As an application of this
result we show that a signed graph $G$ admitting a nowhere-zero $k$-flow has a
covering with signed circuits of total length at most $2(k-1)|E(G)|$.
