The research of the system of linguistic means, which express the strategy of evasion in dialogues within the framework of pragmalinguistics, contributes to a comprehensive study of this phenomenon, meeting the requirements of the nowadays scientific demands. The appeal to this topic is due to insufficient knowledge of the system of linguistic and pragmatic means that realize the strategy of evasion in dialogical speech. The aim of this paper describe the specifics of such language system analyzing some works of G. Ibsen, A. Miller, T. Williams and other well-known modern writers. The paper reveals the specifics of a dialogue as well as the phenomenon of speech influence, whose aim is to convince interlocutors consciously and / or unconsciously to accept someone else's point of view. The authors reveal the realization of the strategy of evasion in the dialogical unity studying some corresponding communicative tactics such as repetitions (including resentment, replay, reproach and overexpression), delay of response and mitigation of categoricity of response. All of them are represented by a great variety of multi-level linguistic means. The identified set of communicative tactics of the evasion strategy makes it possible to understand what communicative actions an addresser can perform to influence the addressee.