The article deals with the process of founding and further development of the new rhetoric, a theory of argumentation developed by the Belgian philosopher Chaïm Perelman (1912-1984) and his co-worker Lucie Olbrechts-Tyteca (1899-1987). The intellectual and philosophical backgrounds of the authors and some key characteristics of their theoretical approaches are described. The new rhetoric: (а) is primarily concerned with argument or practical reasoning, (b) suggests that figures of speech may be arguments instead of merely ornaments, (c) with its goal to influence minds, new rhetoric is a dynamic field of study, (d) it is complimentary rather than in opposition to formal reasoning. According to Perelman, the theory of argumentation conceived as a new rhetoric or dialectic, covers the whole range of discourse that aims at persuasion and conviction, whatever the audience addressed and whatever the subject matter. Perelman presents his new rhetoric as a much better form of logic than Cartesian deductive, stringent reasoning, at least where law and other values-based systems are concerned. Perelman challenged the unwholesome assumption that what we cannot know with mathematical certainly is necessarily arbitrary, irrational, and subjective. Perelman recognized "reasoned conviction" as a bridge to knowledge, although he was aware that it was a less perfect source of cognition than verified certainty. It is explained how the idea of developing the new rhetoric was born out of dissatisfaction with logical positivism or neopositivism (The Vienna Circle’s theories and ideas) and which classical and modern sources inspired the authors in developing a specific logic of value judgments that could deal with argumentation about actions, choices, decisions and without dismissing such argumentation as irrational. The rhetorical framework of the theory is expounded and an overview is provided of the key notions and concepts of Perelman’s ‘new rhetoric’ – the notions of adherence, audience (particular and universal audience), persuasion are explained. According to Perelman, the new rhetoric is based on the idea that since argumentation aims at securing the adherence of those to whom it is addressed, it is, in its entirety, relative to the audience to be influenced. Рerelman's position on the difference between formal logic and argumentation is analyzed.