With restructuring characterising many school systems throughout the world, and major change leaving few schools untouched, school leaders are facing major challenges. This study focuses on a group of Hong Kong principals who conceptualise some of their challenges as dilemmas. The paper draws on previous literature to highlight the importance of articulating principals' perceptions of dilemmas in their daily lives, and identifies typologies and categories of dilemmas. It notes that dilemma research to date is grounded in Western examples and cultural settings, and that dilemmas faced by principals in non-Western settings have been ignored. Analysing dilemma situations recounted by Hong Kong principals, we identify the sources, coping mechanisms and outcomes of their dilemmas and examine the relationships between these phenomena. Among our findings are that dilemmas are multifaceted and irresolvable situations, and that principals tend to rely on a narrow range of deeply embedded Chinese cultural values as coping strategies. Copyright © 2000 Australian Council for Educational Research (ACER).