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To realize continuous-wave (CW) operation of millimeter-wave gyrotrons at megawatt (MW)-power levels, these devices must operate in very high-order modes. To excite such an operating mode and to drive it into the regime of MW-level operation with high efficiency requires careful consideration of the startup scenario through which the operating parameters of the device are brought to their nominal values. In the present paper, several common startup scenarios and the most important physical effects associated with them are discussed. Then, the paper presents the results of startup simulations for a 140-GHz, MW-class gyrotron developed by Communications and Power Industries (CPI) for electron-cyclotron plasma heating and current drive experiments on the "Wendelstein 7-X" stellarator. The simulations were done with MAGY, a multifrequency, self-consistent code developed at the University of Maryland. Simulations tracking six competing modes show that, with a proper choice of operating parameters, stable excitation of the desired TE28,7-mode at 1 MW level can be realized, despite the presence of dangerous parasites in the resonator spectrum. These results are in approximate agreement with experimental tests, in which the gyrotron demonstrated reliable operation at power levels up to 900 kW. PACS numbers: 84.40.Ik, 52.75 Ms.