Pervasive computing is a user-centric mobile computing paradigm, in which tasks should be migrated over different platforms in a shadow-like way when users move around. In this paper, we propose a context-sensitive task migration model that recovers program states and rebinds resources for task migrations based on context semantics through inserting resource description and state description sections in source programs. Based on our model, we design and develop a task migration framework xMozart which extends the Mozart platform in terms of context awareness. Our approach can recover task states and rebind resources in the context-aware way, as well as support multi-modality I/O interactions. The extensive experiments demonstrate that our approach can migrate tasks by resuming them from the last broken points like shadows moving along with the users.