A new type of plasma instability is described in an electron‐beam ionized discharge. This instability occurs in the form of current oscillations in gas mixtures in which the dissociative attachment rate increases strongly with electric field. It has been observed experimentally in He : H2O 74 : 2 and in He : CO21 : 1 and 9 : 1 mixtures. A theoretical analysis which describes the onset of instability is presented, and a physical explanation is given. The region of instability in parameter space of ionization source functionSand electric fieldEis presented for certain gas mixtures. The transient phenomena in this type of discharge appear to be controlled by electron attachment, and a theoretical explanation of the observed current overshoot has been provided.