Directors and boards face many challenges in terms of managing complexity. A key factor of
success in practising good corporate governance is the board’s ability to cope with paradox. The purpose of this research has been to explore the core corporate governance dilemmas facing boards. The investigation was qualitative in nature using the Delphi technique. Six core corporate governance dilemmas facing board members were identified one of which is not mentioned in the international literature. The findings should provide directors with an ability to identify the nature of the paradoxes to which they need to respond.