[en] We present the linear evolution in space-time of electromagnetic instabilities generated by relativistic beam-type electron distribution functions that characterize highly anisotropic electron plasmas. The plasma is assumed to be infinite, homogeneous and in a static, uniform magnetic field (antiB₀). For waves propagating along antiB₀ there are two absolute instabilities - the Whistler and the relativistic instability - both near the electron cyclotron frequency (omega/sub c/). For waves propagating perpendicular to antiB₀ instabilities occur at omega/sub c/ and its harmonics. At low densities the instability at omega/sub c/ is absolute and has the highest growth rate, while those at higher harmonics are convective and have lower growth rates. As the density is increased the instabilities at omega/sub c/ and 2omega/sub c/ are absolute. Further increase in the density leads to the instability at omega/sub c/ becoming convective and that at 2omega/sub c/ remaining absolute. The detailed observation of unstable radiation from such plasmas could lead to an estimate of the hot density component of the plasma. In another context, gyrotron-type devices could conceivably be built for generating electromagnetic energy at harmonics of omega/sub c/