A search for heavy right-handed Majorana or Dirac neutrinos (NR) and heavy right-handed W gauge bosons (WR) participating in the Keung-Senjanovi´c process has been performed in events with a pair of energetic electrons or muons, with opposite-sign charges, and two energetic jets. Events were selected from pp collision data with an integrated luminosity of 36.1fb−1 collected by the ATLAS detector at √s = 13TeV. No significant deviations from the Standard Model expectation were observed. The results were interpreted within the theoretical frameworks of two forms of Left-Right Symmetric Model and lower limits were set on masses in the heavy right-handed W and neutrino mass plane, as well as upper limits on the Keung-Senjanovi´c process cross section multiplied by the branching fraction to eejj or µµjj. The excluded region extends to mWR = 4.7TeV for both Majorana and Dirac NR neutrinos. The mNR > mWR region is explored for the first time by a search for the Keung-Senjanovi´c process at the LHC.