Let $\gamma '_{s} $(G) and $\gamma'_{l} $(G) be the numbers of the signed edge and local signed edge domination of a graph G [2], respectively. In this paper we prove mainly that $\gamma '_{s}(G)\le \lfloor{\frac{{11}}{{6}}n - 1}\rfloor$ and $\gamma'_{l}(G)\le 2n-4$ hold for any graph $G$ of order $n (n\ge 4)$, and pose several open problems and conjectures.
