Dispersion characteristics have been analysed for field-aligned electron–cyclotron waves (also known as right-hand polarized waves, extraordinary waves or whistlers) in a cylindrical magnetic mirror plasma including electrons with anisotropic temperature. It is shown that the instability of these waves is possible only in the range below the minimal electron–cyclotron frequency, which is much lower than the gyrotron frequency used for electron–cyclotron resonance power input into the plasma, under the condition where the perpendicular temperature of the resonant electrons is larger than their parallel temperature. The growth rates of whistler instability in the two magnetized plasma models, where the stationary magnetic field is either uniform or has a non-uniform magnetic mirror configuration, are compared.