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In contrast to ordinary graphs, the number of the nowhere-zero group-flows in a signed graph may vary with different groups, even if the groups have the same order. In fact, for a signed graph G and non-negative integer d, it was shown that there exists a polynomial F d (G, x) such that the number of the nowhere-zero Γ-flows in G equals F d (G, x) evaluated at k for every Abelian group Γ of order k with ǫ(Γ) = d, where ǫ(Γ) is the largest integer d for which Γ has a subgroup isomorphic to Z d 2 . We focus on the combinatorial structure of Γ-flows in a signed graph and the coefficients in F d (G, x). We first define the fundamental directed circuits for a signed graph G and show that all Γ-flows (not necessarily nowhere-zero) in G can be generated by these circuits. It turns out that all Γ-flows in G can be evenly classified into 2 ǫ(Γ) -classes specified by the elements of order 2 in Γ, each class of which consists of the same number of flows depending only on the order of the group. This gives an explanation for why the number of Γ-flows in a signed graph varies with different ǫ(Γ), and also gives an answer to a problem posed by Beck and Zaslavsky. Secondly, using an extension of Whitney's broken circuit theory we give a combinatorial interpretation of the coefficients in F d (G, x) for d = 0, in terms of the broken bonds. As an example, we give an analytic expression of F 0 (G, x) for a class of the signed graphs that contain no balanced circuit. Finally, we show that the sets of edges in a signed graph that contain no broken bond form a homogeneous simplicial complex.