In this paper a comprehensive kinetic, gyrokinetics theory is presented to provide a unified description of transverse‐magnetic‐mode gyrotron, gyropeniotron, cyclotron autoresonance maser, and nonwiggler free‐electron laser amplifiers. By introducing gyrokinetic variables, a unified dispersion equation is derived in which the effect of the guiding‐center shift is taken into account. Similar to the transverse‐electric‐mode cases, it is found that at the zero point of theJm−l(R¯) instability is still effective, whereJm−lis the Bessel function of order (m−l),mandlare, respectively, the azimuthal index of the mode and the index of the synchronous harmonic, andR¯ is the electron beam radius normalized by the cutoff wavenumber.