Let G = (V,E), V = {v1, v2,…, vn} be a simple connected graph with n vertices, m edges and a sequence of vertex degrees d1 ≥ d2 ≥ ··· ≥ dn > 0, di = d(vi). The general sumconnectivity coindex is defined as Ha(G) = ∑i j (di + dj) a , while multiplicative first Zagreb coindex is defined as P1(G) = ∏i j (di + dj). Here a is an arbitrary real number, and i j denotes that vertices i and j are not adjacent. Some relations between Ha(G) and P1(G) are obtained.