We study theoretically models of gyrotrons having fixed and self-consistent axial structures of the high-frequency field in the cavity with an actual profile. The limits of applicability of the model with a given field structure are determined during the study of competition of the operating and parasitic modes. It is shown that for the regimes which are optimal in terms of efficiency, the influence of the nonfixed nature of the high-frequency field structure on the starting current, the stability of stationary generation of the operating mode, the efficiency, the output power, and the thermal ohmic load of the cavity is insignificant. As the beam current and the mismatch between the cutoff frequencies of the operating and parasitic modes increase, significant qualitative differences between the models with given and self-consistent axial structures of the high-frequency field are observed.