A simplified formalism has been developed for calculating the minimum starting currents of gyrotron modes, as well as the sequence of gyrotron modes excited as a function of resonator magnetic field. Unlike treatments ihich assume that modes are excited at the Doppler-shifted cyclotron frequency, this analysis is in good agreement with the exact solution of gyrotron linear theory. It is shown that each TEmpq mode is characterized by q strong excitation branches, and of these branches two predominate for q > 2. For the case of q = 1, only a single branch at the Doppler down-shifted frequency is strong. 'The cyclotron frequencies at which these branches are excited are found to vary with q, but their minimum starting currents are roughly independent of q if Q does not depend on q. A simple technique for constructing mode spectra is presented, and examples are given for the TE 0 3 1 and TE521 modes. In addition the effect of the time-varying gun voltages on the mode excitation spectra during the turn-on phase of a pulsed gyrotron has been investigated. The method in which the cathode and control anode voltages of the gun are increased to their final operating values can significantly affect which modes are excited in a gyrotron. Of the two startup procedures analyzed in detail, it was found that holding the cathode voltage steady at its final value while ramping-up the anode voltage helped to minimize the appearance of parasitic