The framework of Temporal constraint Satisfaction Problems (TCSP) has been proposed for representing and processing temporal knowledge. Deciding consistency of TC-SPs is known to be intractable. As demonstrates in this paper, even local consistency algorithms like path-consistency can be exponential due to the fragmentation problem. We present t wo new polynomial approximation algorithms, Upper-Lower-Tightening (ULT) and Loose-Path-Consistency (LPC), which are ecient y et eective in detecting inconsistencies and reducing fragmentation. The experiments we performed on hard problems in the transition region show that LPC is the superior algorithm. When incorporated within backtrack search LPC is capable of improving performance by orders of magnitude. Problems involving temporal constraints arise in various areas such as temporal databases [6], diagnosis [11], scheduling [22, 2 1 ], planning [16], common-sense reasoning [25] and natural language understanding [1]. Several formalisms for expressing and reasoning about temporal constraints have been proposed; interval algebra [2], point algebra [29], Temporal Constraint Satisfaction Problems (TCSP) [7] and the model of combined quantitative and qualitative constraints [17, 12].The two t ypes of Temporal Constraint Networks that have emerged are qualitative [2] and quantitative [7]. In the qualitative model, variables are time intervals and the constraints are qualitative. In the quantitative model, variables represent time points and the constraints are metric. Subsequently, these two t ypes were combined into a single model [17,12]. In this paper we build upon the model proposed by [17], whose variables are either points or intervals and involves three types of constraints: metric point-point and qualitative pointinterval and interval-interval.Answering queries in constraint processing reduces to the tasks of determining consistency, computing a consistent scenario and computing the minimal network. When time is represented by rational numbers 1 , deciding consistency is in NP-complete [7,17]. For qualitative networks, computing the minimal network is in NP-hard [10,7]. In both qualitative and quantitative models, the source of complexity stems from allowing disjunctive relationships between pairs of variables. Such constraints often arise in many applications, as demonstrated by the following example: