A new surface wave instability is derived for a magnetically confined pure electron gas column with density34<2&ohgr;p02/&OHgr;02<1. The equilibrium configuration consists of two superimposed electron beams aligned parallel to the confining magnetic fieldB0, and rotating with different azimuthal velocities about the axis of symmetry. The instability, which is of the two‐stream form, results from the interaction of surface waves on each of the two superimposed beams.