A temporal constraint management system (TCMS) is a temporal network together with algorithms for managing the constraints in that network over time. This paper presents a practical TCMS, called MYSYSTEM, that efficiently handles the propagation of the kinds of temporal constraints commonly found in realtime applications, while providing constant-time access to "all-pairs, shortest-path" information that is extremely useful in many applications. The temporal network in MYSYSTEM includes special timepoints for dealing with the passage of time and eliminating the need for certain common forms of constraint propagation. The constraint propagation algorithm in MYSYSTEM maintains a restricted set of entries in the associated all-pairs, shortest-path matrix by incrementally propagating changes to the network either from adding a new constraint or strengthening, weakening or deleting an existing constraint. The paper presents empirical evidence to support the claim that MYSYSTEM is ...