  This paper reports searches for heavy resonances decaying into $ZZ$ or $ZW$
using data from proton--proton collisions at a centre-of-mass energy of
$\sqrt{s}=13$ TeV. The data, corresponding to an integrated luminosity of 36.1
fb$^{-1}$, were recorded with the ATLAS detector in 2015 and 2016 at the Large
Hadron Collider. The searches are performed in final states in which one $Z$
boson decays into either a pair of light charged leptons (electrons and muons)
or a pair of neutrinos, and the associated $W$ boson or the other $Z$ boson
decays hadronically. No evidence of the production of heavy resonances is
observed. Upper bounds on the production cross sections of heavy resonances
times their decay branching ratios to $ZZ$ or $ZW$ are derived in the mass
range 300--5000 GeV within the context of Standard Model extensions with
additional Higgs bosons, a heavy vector triplet or warped extra dimensions.
Production through gluon--gluon fusion, Drell--Yan or vector-boson fusion are
considered, depending on the assumed model.
