The classical double-stream theory for electrostatic instabilities in a cold plasma is generalized by a more complete treatment of the electrodynamics, whereby an analysis of electromagnetic instabilities is now afforded. Thus, consideration of wave propagation at arbitrary angles to the stream or drift motion leads to a rather involved sixth-degree algebraic dispersion formula which reflects the possible occurrence of coupled growing longitudinal and transverse waves. It is further evidenced that electromagnetic instabilities may arise even in a single-carrier system such as an electron beam. Like the special alignment where the stream and wave vectors are parallel (U\ensuremath{\parallel}k), the orthogonal case (U \ensuremath{\perp} k) fails to allow growing transverse waves for the single-carrier stream. However, this latter configuration does admit electromagnetic instabilities for the double-stream plasma; likely unstable regimes are indicated. A more plausible basis for interpreting radiowave emission from plasmas emerges, and solar noise, for example, may be viewed as a direct consequence of such electromagnetic-wave instabilities.