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.