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The stability of time-domain simulations is examined for a generalized lossy double-negative transmission line (TL). This is accomplished using a "modified" version of the Courant-Friedrichs-Lewy stability criterion. The time-domain simulation is implemented using a method-of-moments formulation with the generalized TL equations. An analytic expression is derived by combining the Z-transform with von Neumann methods. The credibility of simulated time-domain results is verified through comparison with modal behavior determined using a frequency-domain treatment for a periodic structure.