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Cloud computing, a new paradigm of distributed computing, introduces many new ideas, concepts, principals, technologies and architectural styles into enterprise service-oriented computing. The enterprise service-oriented architecture (ESOA) style is an abstraction of concrete enterprise service-orientated architectures, which includes SOA architectural elements, service design patterns as well as principles, and SOA quality attributes. It can be extended to a new style for realizing enterprise cloud computing. Meanwhile, the principles and style of enterprise service-oriented computing facilitate the enterprise-wide adoption of cloud computing. This paper extends the ESOA style to a new hybrid architectural style, Enterprise Cloud Service Architecture (ECSA). The style is described by extending enterprise service-oriented formula for ESOA. We model the style through specifying each element in the formula with both service-oriented and cloud architectural styles.