We consider the dispersion relation for waves in a cosmic ray modified plasma for the case when the background flow consists of a cosmic ray pressure balance structure, in whichpg+pc=const.wherepcandpgdenote the cosmic ray and thermal gas pressures respectively. The stability analysis shows that waves at an arbitrary point in the flow may be driven unstable if the cosmic ray pressure gradient is sufficiently large to overcome wave damping due to cosmic ray diffusion. Following S. Chalov’s work (1) we analyze the instability of a cosmic ray modified tangential discontinuity. Chalov considered the case wherepc=const.throughout the structure, whereas in our analysis bothpcandpgvary in the direction perpendicular to the surface separating two flow regions. Predictions of the linear theory are compared to numerical simulations. Applications to the stability of the heliopause are discussed. ©1999 American Institute of Physics.