This paper examines the nature of the core capabilities of a firm, focusing in particular on their interaction with new product and process development projects. Two new concepts about core capabilities are explored here. First, while core capabilities are traditionally treated as clusters of distinct technical systems, skills, and managerial systems, these dimensions of capabilities are deeply rooted in values, which constitute an often overlooked but critical fourth dimension. Second, traditional core capabilities have a down side that inhibits innovation, here called core rigidities. Managers of new product and process development projects thus face a paradox: how to take advantage of core capabilities without being hampered by their dysfunctional flip side. Such projects play an important role in emerging strategies by highlighting the need for change and leading the way. Twenty case studies of new product and process development projects in five firms provide illustrative data.