The article presents an attempt to develop a project of a special version of dialectics – dialectics of the remainder. After Sl. Žižek, the authors believe that there may exist a dialectic, different from both Hegelian, positive, and T. Adorno’s negative dialectics. This dialectics appears as a result of the impossibility to divide the world, man and society into opposites – without a remainder. The remainder is a kind of "negative product" of socio-cultural changes that encourage thinking of marginal, adverse, peripheral phenomena as becoming something more significant in the dynamics of contemporary society. There are many contemporary social and aesthetic processes conforming to the remainder principle. A historical event can be represented as a significant remainder of many actions, forces and wills intertwined in the historical process. Many new artistic and aesthetic forms look like remainders of previous forms – classical or modern. Such a remaining remainder of classical and non-classical art today is social actionism. As a method, the research work used the dialectical approach to dialectics itself, as well as the principle of its historical deconstruction. As a result, the author discovered a special version of dialectics that can be referred to as "dialectics of the remainder".Keywords: dialectics, dialectics of the remainder, organ, social-aesthetic phenomena, social actionism.