Abstract : UML goal of being a general-purpose modeling language discards the possibility to adopt too precise and strict a semantics. Users are to refine or define the semantics in their domain specific profiles. In the UML Profile for Modeling and Analysis of Real-Time and Embedded systems, we have defined a broadly expressive Time Model to provide a generic timed interpretation for UML models. Our clock constraint specification language supports the specification of systems with multiple clock domains. Starting with a priori independent clocks, we progressively compose them to get a family of possible executions. Our language supports both synchronous and asynchronous compositions, just like the synchronous language Signal, but also allows explicit non determinism. In this paper, we give a formal semantics to a core subset of MARTE clock constraint languages and we give an equivalent interpretation of this kernel in two other very different formal languages, Signal and Time Petri Nets.