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We propose a template-based approach to structuring the semantics of model-based specification notations. The basic computation model is a nonconcurrent, hierarchical state-transition machine (HTS), whose execution semantics are parameterized. Semantics that are common among notations (e.g., the concept of an enabled transition) are captured in the template, and a notation's distinct semantics (e.g., which states can enable transitions) are specified as parameters. The template semantics of composition operators define how multiple HTSs execute concurrently and how they communicate and synchronize with each other by exchanging events and data. The definitions of these operators use the template parameters to preserve notation-specific behavior in composition. Our template is sufficient to capture the semantics of basic transition systems, CSP, CCS, basic LOTOS, a subset of SDL88, and a variety of statecharts notations. We believe that a description of a notation's semantics using our template can be used as input to a tool that automatically generates formal analysis tools.