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 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 300-5000GeV 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.[Figure not available: see fulltext.].