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High power gyrotrons, including both CW and high peak power configurations, are increasingly designed to operate in high mode density regimes. It has been observed that operation is often single-moded even for cavities with dense mode spectra, but the mode density does affect the gyrotron efficiency and the available operating modes. Multimode effects have been studied extensively for the quasi-optical gyrotron but there has been less progress on fully nonlinear formulations for conventional waveguide cavity gyrotrons which involve different transverse modes with irregularly spaced frequencies and unequal coupling impedances. A time-dependent, nonlinear, multimode theory of gyrotrons has been recently developed along with a computer code to carry out the numerical calculations. The code has been used to simulate the operation of a CW-relevant 140 GHz gyrotron experiment carried out at MIT and the 750 kV, 35 GHz intense-beam gyrotron experiment at NRL. The MIT gyrotron involves competition between two transverse modes: the TE03 and TE23 modes. The NRL gyrotron involves competition between TEm2 modes and is an example of a three-mode interaction.