Let G be an undirected connected graph with n, n ≥ 3, vertices and m edges. If μ1 ≥ μ2 … ≥ μn-1 > μn = 0 and ρ1 ≥ ρ2 ≥ …≥ ρn-1 > ρn = 0 are the Laplacian and the normalized Laplacian eigenvalues of G, then the Kirchhoff and the degree Kirchhoff indices obey the relations K ƒ (G) = nΣn-1 i=1 μ-1 i and DK ƒ (G) = 2mΣn-1 i=1 ρ-1 i-1, respectively. The inequalities that determine lower bounds for some invariants of G, that contain K ƒ (G) and DK ƒ (G), are obtained in this paper. Lower bounds for K ƒ (G) and DK ƒ (G), known in the literature, are obtained as a special case.