Background: The effect of conservative vs. liberal oxygen therapy on outcomes of intensive care unit (ICU) patients with hypoxic ischaemic encephalopathy (HIE) is uncertain and will be evaluated in the Low Oxygen Intervention for Cardiac Arrest injury Limitation (LOGICAL) trial. Objective: The objective of this study was to summarise the protocol and statistical analysis plans for the LOGICAL trial. Design, setting, and participants: LOGICAL is a randomised clinical trial in adults in the ICU who are comatose with suspected HIE (i.e., those who have not obeyed commands following return of spontaneous circulation after a cardiac arrest where there is clinical concern about possible brain damage). The LOGICAL trial will include 1400 participants and is being conducted as a substudy of the Mega Randomised registry trial comparing conservative vs. liberal oxygenation targets in adults receiving unplanned invasive mechanical ventilation in the ICU (Mega-ROX). Main outcome measures: The primary outcome is survival with favourable neurological function at 180 days after randomisation as measured with the Extended Glasgow Outcome Scale (GOS-E). A favourable neurological outcome will be defined as a GOS-E score of lower moderate disability or better (i.e. a GOS-E score of 5–8). Secondary outcomes include survival time, day 180 mortality, duration of invasive mechanical ventilation, ICU length of stay, hospital length of stay, the proportion of patients discharged home, quality of life assessed at day 180 using the EQ-5D-5L, and cognitive function assessed at day 180 using the Montreal Cognitive Assessment (MoCA-blind). Conclusions: The LOGICAL trial will provide reliable data on the impact of conservative vs. liberal oxygen therapy in ICU patients with suspected HIE following resuscitation from a cardiac arrest. Prepublication of the LOGICAL protocol and statistical analysis plan prior to trial conclusion will reduce the potential for outcome-reporting or analysis bias. Trial registration: Australian and New Zealand Clinical Trials Registry (ACTRN12621000518864).