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The intention of this paper is to extend our generic component framework presented at FASE 2002 [H. Ehrig, F. Orejas, B. Braatz, M. Klein, and M. Piirainen. A generic component concept for system modeling. In Proc. FASE '02, LNCS 2306. Springer, 2002] to a specific kind of connector architectures similar to architectural connections in the sense of Allen and Garlan [ACM Transactions on Software Engineering and Methodology, 1997]. In our generic component framework we have considered components with explicit import, export and body parts connected by embeddings and transformations and composition of components with a compositional transformation semantics. Our framework, however, was restricted to components with a single import and export interface. Here we study architectures based on connectors with multiple imports and components with multiple exports. Architectures studied in this paper are built up from components and connectors in a noncircular way. The semantics of an architecture is defined by reduction step sequences in the sense of graph reductions. The main result shows existence and uniqueness of the semantics of an architecture as a normal form of reduction step sequences. Our generic framework is instantiated on one hand to connector architectures based on CSP as the formal specification technique in the approach by Allen and Garlan. On the other hand it is instantiated to connector architectures based on high-level-replacement systems in general and Petri nets in particular. A running example using Petri nets as modeling technique illustrates all concepts and results.