Much research has been published on risk management, business continuity, crisis committees and resilience. There is not a day in the press when an event requiring crisis management is not reported. We have therefore taken an interest in the composition of a crisis team. To this end, we conducted semi-directive interviews to understand what were the important elements in the composition of a crisis team to better manage the unexpected. It appears that experience takes precedence over the hierarchical level of the involved individuals. It even seems preferable not to involve or at least to limit the number of members of the upper management. Although our study shows the benefits of simulations, stress test scenarios, the composition of the crisis team has to be better integrated especially to take into account emerging risks such as cyberattacks where improvisation plays a crucial role.