  A search for neutral heavy resonances is performed in the $WW\to e\nu\mu\nu$
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 $\sigma_X \times
B(X \to WW)$ 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.
