For an arbitrary graph G, the IRREGULARITY and total IRREGULARITY of G are defined as irr(G) = åuvÎE(G) |dG(u) − dG(v)| and irrt(G)=1/2åu,vÎv(g) |dG(u)− dG(v)|, respectively, where dG(u) is the degree of vertex u. In this paper, we characterize all connected Eulerian graphs with the second minimum IRREGULARITY, the second and third minimum total IRREGULARITY, respectively.