We consider the problem of minimizing the differential delay in a virtually concatenated Ethernet-over-SONET (EoS) system by suitable path selection. In such a system, a service provider can dynamically add virtual channels to or drop them from a Virtually Concatenated Group (VCG). A new virtual channel can be added to the VCG provided that the differential delays between the new channel and the existing ones are within a certain limit that reflects the available memory buffer of the EoS system. We model the problem of finding such a virtual channel as a constrained path selection problem, where the delay of the required (feasible) path is constrained not only by an upper bound but also by a lower bound. We consider two cases: exactly known link delays and imprecisely known link delays. For the first case, we propose two algorithms for finding a feasible path. The first is based on a link metric that linearly combines the original link weight (the link delay) and its inverse. The theoretical properties of such a metric are studied and used to develop a highly efficient heuristic for path selection. The second algorithm is a “backward–forward” heuristic in which the nodes in the graph are prelabeled during the backward phase. The labels are then used in the forward phase to identify a feasible path. For the imprecise-link-state case, the problem is modeled as one of finding the most probable feasible path, where link weights are random variables. A “backward–forward” heuristic is proposed which again uses prelabeling of the graph in the backward direction followed by a forward search that attempts to minimize an objective function. Simulations are conducted to evaluate the performance of the proposed algorithms and to demonstrate the advantages of the probabilistic path selection approach over the classic trigger-based approach.