The Clock Constraint Specification Language (CCSL) has been informally introduced in the specifications of the UML Profile for Modeling and Analysis of Real-Time and Embedded systems (MARTE). In a previous report entitled ``Syntax and Semantics of the Clock Constraint Specification Language'', we equipped a kernel of CCSL with an operational semantics. In the present report we pursue this clarification effort by giving a mathematical characterization to each CCSL constructs. We also propose a systematic approach to the formal verification of CCSL constraints with dedicated Observers. A comprehensive library of Esterel modules, which supports this approach, is provided.