Transverse electromagnetic waves that propagate along a uniform magnetic field in an unbounded, thermally anisotropic plasma are investigated. The linearized Vlasov equation is solved to obtain the dispersion relation for the electron‐ and ion‐cyclotron waves. This dispersion relation is used to determine the critical frequencies and wavenumbers below which the wave is unstable. The electron‐cylotron wave is unstable forT⊥e>Tze. Numerical solutions for the growth and damping rates of the waves obtained from the dispersion relation show that the maximum growth rate occurs at a frequency slightly below the marginally stable frequency. For the ion‐cyclotron wave, both ion and electron thermal anisotropy are included, and cold electrons are shown to have a stabilizing influence on an unstable ion‐cyclotron wave; however, when the electrons are thermally anisotropic, they have a destabilizing effect forT⊥e>Tze.