Linearized equations are set up to describe the effect of an electrostatic wave on an anisotropic relativistic proton plasma embedded in a homogeneous magnetic field. It is assumed that a cold background plasma of protons and electrons co‐exists with the relativistic plasma. It is shown that instability arises whenever the relativistic proton plasma is anisotropic in the right sense. It is also shown that the growth rates are physically significant for galactic cosmic rays and thus space‐charge waves are a mechanism for producing some measure of isotropy in an anisotropic cosmic ray distribution. For instance, 10% anisotropy yields ane‐folding time of about 103years.