Dispersion relations have been derived for field-aligned cyclotron waves in the two-dimensional axisymmetric mirror-trapped plasma models with anisotropic temperature. The transverse dielectric characteristics are evaluated by solving the Vlasov equations for charged particles in the zero-order of magnetization parameters taking into account the cyclotron and bounce resonances for the straight mirror traps, inner part of the Earth's magnetosphere and laboratory magnetic dipole plasmas. The steady-state Maxwellian and bi-Maxwellian distribution functions of plasma particles are considered.