Uncertainty is a fact of project life. Most decisions that are made on a safety-critical project involve uncertainty, the consequences of which may be highly significant to the safe and timely delivery of the project. Based on interviews with project management practitioners on 9 large-scale civil nuclear and aerospace projects, we explore how uncertainty emerges, and how project management practitioners identify, analyse and act on it. We make three important contributions. First, we present three approaches -structural, behavioural and relational -that individuals and organisations can adopt when contending with project uncertainty. Secondly, we characterise nine dualities at play in the management of project uncertainty and thirdly we identify key differences between how civil nuclear and aerospace project managers confront project uncertainty, which have important implications for how projects might be organised in both these industry sectors. Drawing attention to the structural, behavioural and relational approaches to project uncertainty and the tensions that manifest themselves in each approach should enable the project management community to make progress in environments of high uncertainty where situations are often complex, rapidly changing and confusing, and yet where, for reasons of safety, failure is not an option.