Let G be a graph with p vertices and q edges. A bijection f from V(G) U E(G) to {1, 2, …, p + q} is called an edge-magic labeling of G if there exists a constant k(f ) such that f(u) + f(v) + f(uv) = k(f ) for any edge uv of G. In such a case, G is said to be edge-magic. Moreover, f is a super edge-magic labeling of G if F(V(G)) = {1, 2, …, p} and G is said to be super edge-magic. The super magic strength of G, denoted by sm(G) is defined as the minimum of all k(f ), where the minimum is taken over all super edge-magic labelings of G. In this paper, we study some new classes of super edge-magic graphs and their super magic strengths.