A current‐carrying electron‐proton plasma is studied by calculating the velocity distribution of the particles with the Lenard‐Balescu‐Guernsey form of the Fokker‐Planck equations rather than with the familiar Landau form. The Landau equations yield velocity distributions that become unstable to longitudinal ion waves when the temperature ratioTe/Tiis large and the electric fieldE0that drives the current exceeds a critical magnitudeEcrit. The Landau equations are then not appropriate because they do not include the effect that the fluctuations associated with these ion waves have upon the velocity distributions. The Lenard‐Balescu‐Guernsey equations show that asE0is increased towardEcritthese fluctuations increase and affect the electron velocity distribution much as enhanced electron‐electron collisions would do. In particular, this nonlinear process reduces the electrical conductivity by a noticeable amount (a few percent in the examples given). Although one might also expect the threshold electric field for instability to be increased significantly, this effect is found to be extremely weak, if it exists.