A new model for simulating gyrotron oscillators in the monomode time-dependent linear self-consistent regime is presented. Starting from a nonlinear time-dependent monomode model, the linearization and the following simplification of the model, based on a moment approach, are described. This simplified model represents a numerically efficient model and allows to have a deeper physical insight, in particular, for regimes dominated by self-consistent effects such as for the gyro-backward wave instability. One specific case of a gyrotron cavity is studied in detail and compared with experimental results, with special attention to self-consistent effects and to the differences with a model using a fixed field profile. Self-consistent linear simulations are, amongst other applications, important for the design of frequency-tunable gyrotrons or high-power gyrotrons with cavities having a relatively low quality factor, but also for studies of parasitic oscillations as they may occur in beam ducts and/or in the launcher section following the interaction cavity. (C) 2014 AIP Publishing LLC.