ORIENTATION: With uncertainty increasingly defining organisational contexts, executive leaders need to develop their 'capability for uncertainty' - the ability to engage with uncertainty in their organisational context and to lead others, while simultaneously managing their own experience of uncertainty. However, what constitutes such a holistic 'capability for uncertainty' is not clear. RESEARCH PURPOSE: The purpose was to gain an understanding of what constitutes a capability for uncertainty. MOTIVATION FOR THE STUDY: Gaining an understanding of what components constitute leaders' capability for uncertainty would provide a basis for determining what interventions would be relevant for developing leaders towards achieving such a capability. Research approach, design and method: An interpretive qualitative approach was adopted, using interpretative phenomenological analysis to gain an understanding of what capability executive leaders developed through their lived experience of uncertainty. Two purposive samples of six executive leaders from two different South African companies (a private company and a state-owned company), which had both been experiencing long-term organisational uncertainty prior to and up to the time of the study, were used. Data were collected through semi-structured interviews. MAIN FINDINGS: The executives all developed their capability for uncertainty through lived experiences of uncertainty, to a greater or lesser extent. Five components were identified as constituting a holistic capability for uncertainty, as follows: a sense of positive identity, an acceptance of uncertainty, effective sense-making, learning agility and relevant leadership practices during organisational uncertainty. PRACTICAL/MANAGERIAL IMPLICATIONS: Organisations need to target and design leader development interventions to specifically develop these components of a holistic capability for uncertainty in executives and leaders, enabling them to engage more effectively with uncertainty and to more positively manage their experience of uncertainty in these increasingly turbulent times. CONTRIBUTION/VALUE-ADD: The key contribution is the identification of five crucial components constituting a capability for uncertainty, which can be used to inform leadership development interventions designed to develop such capability in leaders.