as considered in, e.g., [@veraart2017distress; @barucca2016valuation] rather than payments as originally studied in [@EN01]. In Section \[sec:discrete\] we propose a discrete-time formulation for the Eisenberg-Noe model. In discrete time we provide results on existence and uniqueness, as well as a numerical algorithm based on the fictitious default algorithm of [@EN01]. We then extend our model to a continuous-time setting in Section \[sec:continuous\]. For continuous time we consider existence and uniqueness of the clearing solutions, and a numerical algorithm for finding sample paths of this clearing solution, under cash flows modeled by Itô processes. We additionally provide conditions for the discrete-time setting to converge to the continuous-time solution as the time step limits to 0. Section \[sec:discussion\] provides discussion on the financial implications of time dynamics in interbank networks. In particular, we find that the static Eisenberg-Noe clearing solution can be recovered in the continuous-time setting by choosing the network parameters precisely. This allows for a notion of determining the true order of defaults as opposed to the fictitious default order discussed in the static literature based on [@EN01]. However, if the continuous-time network parameters are determined to not follow the rules for recreating the static Eisenberg-Noe setting, then the dynamic 