$L: {\mathbb{T}}\to {\mathbb{R}}^{(n+1) \times (n+1)}_+$ to be functions of the clearing time, i.e., as assets and liabilities with different maturities. The external cash in-flows and nominal liabilities can explicitly depend on the clearing results of the prior times (i.e., $x(t,V_{t-1})$ and $L(t,V_{t-1})$) without affecting the existence and uniqueness results we present, but for simplicity of notation we will focus on the case where the external assets and nominal liabilities are independent of the health and wealth of the firms. Throughout we are considering the discounted cash flows and liabilities so as to simplify notation. In contrast to the static Eisenberg-Noe framework, herein we need to consider the results of the prior times. In particular, if firm $i$ has positive equity at time $t-1$ (i.e., $V_i(t-1) > 0$) then these additional assets are available to firm $i$ at time $t$ in order to satisfy its obligations. Similarly, if firm $i$ has negative wealth at time $t-1$ (i.e., $V_i(t-1) < 0$) then the debts that the firm has not yet paid will roll-forward in time and be due at the next period. For example, consider a network in which obligations come due throughout the day at, e.g., opening, mid-day, and closing, but 