This paper deals with the radiation characteristics of elementary electric and magnetic dipoles in a homogeneous, anisotropic, cold plasma of infinite extent with a uniform magnetostatic field. The cases treated include the electromagnetic sources taken parallel and perpendicular to the magnetostatic field. In all cases expressions for the field components are obtained which are valid at frequencies well below the ion cyclotron frequency. It is found that electric and magnetic dipole sources when oriented perpendicular to the magnetic field excite both ordinary and extraordinary modes. For the ordinary mode, the waves are guided in both directions within cones of small apex angle aligned with the static field. When the dipole sources are aligned with the magnetic field, it is found that the electric dipole excites only the ordinary mode leading to guided wave propagation, while the magnetic dipole excites only the extraordinary mode. In all cases the waves propagate at Alfvén speed. The radiation characteristics are isotropic for the extraordinary mode excited by the perpendicular electric dipole and are nearly isotropic for the aligned magnetic dipole. For other cases the radiated power is concentrated in opposite directions along the static field.