This paper describes new algorithms for processing quantitative and qualitative Temporal Constraint Satisfaction Problems (TCSP). In contrast to discrete Constraint Satisfaction Problems (CSP), enforcing path-consistency on quantitative TCSP is exponential, due to the fragmentation problem. Identifying the fragmentation problem allows us to design several e cient polynomial algorithms that are e ective for detecting inconsistencies and explicating some implicit constraints. We discuss the tradeo s between their e ectiveness and e ciency both theoretically and empirically.