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In this paper, we discuss the development of a 3-D time-domain formulation and simulation code for modeling inductive output tubes (IOTs). This formulation relies on the integration of equivalent circuit equations in time coupled with the Lorentz force equations for particle trajectories. In the case of IOTs and klystrons, the equivalent circuit is a simple inductance-resistance-capacitance model. The same formulation using the equivalent circuit equations for Curnow cavities has been used to simulate coupled-cavity traveling-wave tubes. The connection between the equivalent circuit equations and the forces on the electrons used in the Lorentz force equations is through a scaling of a radio-frequency (RF) field model in which the amplitude is proportional to the cavity voltage. The RF field model can be obtained analytically [as derived in two dimensions by Kosmahl and Branch] or by means of a field map generated by electromagnetic structure simulators. The electron trajectories are integrated in these RF fields as well as using magnetostatic focusing fields and the space-charge fields. The space-charge fields are obtained by mapping the charge to a grid and then solving Poisson's equation. The new code is called NEMESIS, and we discuss the presently implemented IOT model and future development plans. Data on an IOT under development at Communications and Power Industries (CPI; K5H90W-2) have been provided for benchmarking the simulation. Comparison of NEMESIS with both anticipated performance predictions developed using scaling laws developed in-house at CPI and with actual tube performance has been good, and these comparisons are discussed in detail.