Recent research on firm level productivity and organizational performance has highlighted the importance of complementarity among organizational practices. A number of studies have developed methods to test the existence of complementarity among such organizational variables. However, despite these advances in the study of industrial organization and management, our understanding of the complementarity structures remains sketchy. In this paper, we seek to advance research on this topic by identifying different classes of complementarity structures and developing a testing procedure for each class. A three-level testing procedure is developed to find complementarity structures which can be categorized into four different classes: non-complementarity, critical complementarity, non-critical asymmetric complementarity, and non-critical symmetrical complementarity. The testing method is illustrated by using an empirical illustration of a range of knowledge management (KM) strategies as they impact on knowledge creation processes in organizations.