How do organizations achieve and sustain the process of continuous adaptation and change that is necessary to realize strategic information systems alignment? While research has focused on developing deterministic alignment models and on identifying the factors that contribute to alignment, there is little understanding of the process as it evolves over time. In this paper, we propose that coevolution theory offers the opportunity to explore coevolving interactions, interrelationships, and effects as both IS and business strategies evolve. An initial model of this coevolution is presented that applies the key attributes and concepts of coevolution theory to strategic IS alignment. Future directions for advancing our work are highlighted.