A search for neutral heavy resonances is performed in the WW -> e nu mu nu decay channel using pp collision data corresponding to an integrated luminosity of 36.1 fb(-1), collected at a centre-of-mass energy of 13 TeV by the ATLAS detector at the Large Hadron Collider. No evidence of such heavy resonances is found. In the search for production via the quark-antiquark annihilation or gluon-gluon fusion process, upper limits on sigma(X) x B(X -> WW) as a function of the resonance mass are obtained in the mass range between 200 GeV and up to 5 TeV for various benchmark models: a Higgs-like scalar in different width scenarios, a two-Higgs-doublet model, a heavy vector triplet model, and a warped extra dimensions model. In the vector-boson fusion process, constraints are also obtained on these resonances, as well as on a Higgs boson in the Georgi-Machacek model and a heavy tensor particle coupling only to gauge bosons.