Software integration has been a solution to the problem of connecting dissimilar systems for many years. Integration is still a challenging issue. EAI is defined as the process of integrating enterprise systems with existing applications. Since software integration research has yielded a variety of different concepts, we survey and discuss this terminology. EAI arises as an evolution of the CASE technology approach. The main goal of this work is the modeling of EAI in order to obtain a more organized and unified view of the main aspects involved. The EAI model presented here was constructed extending the known Brown?s Conceptual Model of Integration. One contribution of this paper is the identification of architectural styles and patterns and the specification of a quality model based on the ISO 9126-1 standard for enterprise systems (ES). This quality model specifies the quality characteristics that the systems in the EAI domain should hold.