Abstract: The results of a search for direct pair production of top squarks in events with two opposite-charge leptons (electrons or muons) are reported, using 36.1 fb(-1) of integrated luminosity from proton-proton collisions at root s = 13 TeV collected by the ATLAS detector at the Large Hadron Collider. To cover a range of mass differences between the top squark (t) over tilde and lighter supersymmetric particles, four possible decay modes of the top squark are targeted with dedicated selections: the decay (t) over tilde -> b (chi) over tilde (+/-)(1) into a b-quark and the lightest chargino with (chi) over tilde (+/-)(1) W (chi) over tilde (0)(1),the decay (t) over tilde -> t (chi) over tilde (0)(1) into an on-shell top quark and the lightest neutralino, the three-body decay (t) over tilde -> bW (chi) over tilde (0)(1) and the four-body decay (t) over tilde -> bl nu(chi) over tilde (0)(1). No significant excess of events is observed above the Standard Model background for any selection, and limits on top squarks are set as a function of the (t) over tilde and (chi) over tilde (0)(1) masses. The results exclude at 95% confidence level (t) over tilde masses up to about 720 GeV, extending the exclusion region of supersymmetric parameter space covered by previous searches.