The general time-dependent shortest pair of disjoint paths problem (TD-2SP) can be stated as follows. We are given a graph having m nodes and n arcs along with a designated pair of nodes O and D. Each arc (i, j) has a time-dependent travel delay d ij (t i) that varies with the time of arrival t i at the tail node i of the arc during some horizon interval [0, H]. For values of t i ≥ H, we assume that the delay is static. The problem then is to find a pair of arc-disjoint paths between O and D such that the total travel delay (cost) is minimized. This study analyzes the complexity of the problem TD-2SP and several of its variants, and develops models and algorithms to solve this problem as well as more general versions of it in which the pair of paths is required to be only partially disjoint with respect to certain key arcs in the network. The identification of efficient partially or fully disjoint paths finds applications in transportation networks where judiciously selected multiple paths are required for routing traffic between a given origin O and destination D. For example, in dispatching a pair of hazmat trucks from some origin to a destination, we might require the paths to be disjoint with respect to certain selected arcs in the network (or with respect to all arcs) in order to curtail interaction risks and delays associated with potential accidents, while minimizing total transit costs (assumed proportional to total transit time). Moreover, due to time-varying congestion effects, it is more appropriate to consider time-dependent link travel times in such analyses. Another important application of this problem arises in the context of centralized traffic flow control within the