Suppose G is a finite graph with vertex-set V (G) and edge-set E(G). An edge-magic total labelling on G is a one-to-one map λ from V (G) ∪ E(G) onto the integers 1, 2, . . . , |V (G) ∪ E(G)| with the property that, given any edge (x, y), λ(x) + λ(x, y) + λ(y) = k for some constant k. Such a labelling is called strong if the smallest labels appear on the vertices. In this paper, we investigate the existence of strong edge-magic total labellings of graphs derived from cycles by adding one chord.