Recently several papers have been published in which it was shown that even small relativistic effects (v2/c2<<1) change qualitatively the character of propagation of nonlinear electromagnetic waves-the solitary refraction wave in the supersonic regimes becomes the compressional solitary wave. The author discusses the question of supersonic Langmuir solitary wave stability against the perturbation in the direction perpendicular to the motion or under the angle to it. When studying the question of stability they restricted themselves to the case that the perturbation is slowly-varying in both space and time as compared with the change of the original soliton.