Temporal reasoning has been an active research area for over twenty years, with most work focussing on either enhancing the efficiency of current temporal reasoning algorithms or enriching the existing algebras. However, there has been little research into handling over-constrained temporal problems except to recognise that a problem is over-constrained and then to terminate. As many real-world temporal reasoning problems are inherently over-constrained, particularly in the scheduling domain, there is a significant need for approaches that can handle over-constrained situations. In this thesis, we propose two backtracking algorithms to gain partial solutions to over-constrained temporal problems. We also propose a new representation, the end-point ordering model, to allow the use of local search algorithms for temporal reasoning. Using this model we propose a constraint weighting local search algorithm as well as tabu and random-restart algorithms to gain partial solutions to over-constrained temporal problems. Specifically, the contributions of this thesis are: The introduction and empirical evaluation of two backtracking algorithms to solve over-constrained temporal problems. We provide two backtracking algorithms to close the gap in current temporal research to solve over-constrained problems; The representation of temporal constraint networks using the end-point ordering model. As current representation models are not suited for local search algorithms, we develop a new model such that local search can be applied efficiently to temporal reasoning; The development of a constraint weighting local search algorithm for under-constrained problems. As constraint weighting has proven to be efficient for solving many CSP problems, we implement a constraint weighting algorithm to solve under-constrained temporal problems; An empirical evaluation of constraint weighting local search against traditional backtracking algorithms. We compare the results of a constraint weighting algorithm with traditional backtracking approaches and find that in many cases constraint weighting has superior performance; The development of a constraint weighting local search, tabu search and random-restart local search algorithm for over-constrained temporal problems. We extend our constraint weighting algorithm to solve under-constrained temporal problems as well as implement two other popular local search algorithms: tabu search and random-restart; An empirical evaluation of all three local search algorithms against the two backtracking algorithms. We compare the results of all three local search algorithms with our twobacktracking algorithms for solving over-constrained temporal reasoning problems and find that local search proves to be considerably superior.