The Bhatnagar‐Gross‐Krook equations are used to obtain the steady‐state velocity distribution for a uniform, fully ionized plasma in a dc electric field. The Joule heating of the plasma is assumed to be compensated by volume heat losses such as bremstrahlung. The distribution obtained is far from Maxwellian if the drift velocity is comparable to the thermal velocity of the electrons. Longitudinal oscillations with wave vector in the direction of the field are introduced as a perturbation and their dispersion relation obtained. The stability of the steady state is investigated numerically, and it is found to be unstable for sufficiently high drift velocities, the instability being due to the familiar electron ion two stream interaction. The instability is impeded but not prevented by collisions. We find that the critical drift velocity exceeds that calculated in the collisionless theory by at about 20% in the limit that the electric field and collision frequency approach zero. This difference is attributable to the modification of the velocity distribution function.