This paper deals with the stability of coupled Alfvén and drift-mirror modes in a one dimensionally non-uniform plasma in a gyrokinetic framework. A dispersion relation for the mode is obtained and solved for different values of the coupling parameter, proportional to the square of the radial pressure gradient. Even a weak coupling substantially alters the modes' properties. The frequency of the drift-mirror mode is substantially different from that in the decoupled case the drift-mirror instability can develop for lower values of plasma anisotropy. The weak coupling also causes a decrease in the Alfvén mode frequency and leads to an instability whose growth rate is proportional to the coupling parameter. If the coupling is strong, the notions of the Alfvén and drift-mirror modes lose their meaning since their respective oscillation branches merge and further split at some anisotropy value. Another nomenclature is suggested, the unstable and stable Alfvén-mirror modes, the former being unstable at any anisotropy value, and the latter, in contrast, is always damped. Another effect of coupling is the transverse dispersion of the modes, that is, the dependence of the wave frequency on the wave vector transverse component. This effect can be responsible for the mode structure across the magnetic field and perpendicular energy transfer.
Damping and drive of low-frequency modes in tokamak plasmas