The geometric-arithmetic and atom-bond connectivity indices are of interesting and applied indices in the chemical graph theory. Let G = (V, E) be a simple, undirected and connected graph with vertex set V and edge set E. The second geometric-arithmetic and second atom-bond connectivity indices of a graph G are defined as, GA(2) (G) = Sigma (uv is an element of E(G)) 2 root n(u)n(v)/n(u) + n(v), ABC(2) (G) = Sigma(uvE(G)) root n(u) + n(v) - 2 / n(u)n(v), where n(u) is the number of vertices of graph G lying closer to u and n(v) is the number of vertices of graph G lying closer to v. In this paper, we intend to demonstrate the relations between second geometric-arithmetic index and second atom-bond connectivity index for general and special class of graphs.