The edge Szeged index and edge-vertex Szeged index of a graph are defined as Sze(G) =∑ uv∈E(G) mu(uv|G)mv(uv|G) and Szev(G) = 12 ∑ uv∈E(G) [nu(uv|G)mv(uv|G) + nv(uv|G)mu(uv|G)], respectively, where mu(uv|G) (resp., mv(uv|G)) and nu(uv|G) (resp., nv(uv|G)) are the number of edges and vertices whose distance to vertex u (resp., v) is smaller than the distance to vertex v (resp., u), respectively. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, the lower bounds of edge Szeged index and edge-vertex Szeged index for cacti with order n and k cycles are determined, and all the graphs that achieve the lower bounds are identified.