A new type of plasma instability is described in an electron‐beam ionized discharge. This instability occurs in gas mixtures in which the dissociative attachment rate increases strongly with electric field. It has been observed experimentally in He:H2O 740:20 and in He:CO21:1 and 9:1 mixtures. The values of the ionization source functionSand of the electric fieldEat which the wave instability occurs are predicted using a Fourier analysis of the linearized kinetic rate equations. This yields the condition for instability asS< (1/&agr;)[E&dgr;&bgr;/&dgr;E) − &bgr;]2, where &agr; is the electron‐ion recombination coefficient and &bgr; is the electron neutral attachment rate.