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Context-aware web services have been attracting significant attention as an important approach for improving the usability of web services. In this paper, we explore a novel approach to model dynamic behaviors of interacting context-aware web services, aiming to effectively process and take advantage of contexts and realize behavior adaptation of web services and further to facilitate the development of context-aware application of web services. We present an interaction model of context-aware web services based on context-aware process network (CAPN), which is a data-flow and channel-based model of cooperative computation. The CAPN is extended to context-aware web service network by introducing a kind of sensor processes, which is used to catch contextual data from external environment. Through modeling the register link's behaviors, we present how a web service can respond to its context changes dynamically. The formal behavior semantics of our model is described by calculus of communicating systems process algebra. The behavior adaptation and context awareness in our model are discussed. An eXtensible Markup Language-formatted service behavior description language named BML4WS is designed to describe behaviors and behavior adaptation of interacting context-aware web services. Finally, an application case is demonstrated to illustrate the proposed model how to adapt context changes and describe service behaviors and their changes.