The paper studies edge-coloring of signed multigraphs and extends classical Theorems of Shannon and König to signed multigraphs. We prove that the chromatic index of a signed multigraph $(G,σ_G)$ is at most $\lfloor \frac{3}{2} Δ(G) \rfloor$. Furthermore, the chromatic index of a balanced signed multigraph $(H,σ_H)$ is at most $Δ(H) + 1$ and the balanced signed multigraphs with chromatic index $Δ(H)$ are characterized.