The starting point of the path to alternative logics can be found in vague sensations related to the feelings of imperfection of the classical logic and of Aristotelian logic laws. Intense fermentation of logical minds in early XX century Russia created the milieu favorable for the birth of the new type of logics. 1. Due to pretty tight ties with the Western Universities Russian scholars knew well and followed novel trends in logic. However the Russian logical thought developed to large extent along the original lines. In 1901 – 1902 S.O.Shatunovskii argued that the law of excluded middle is not applicative to the infinite sets. In the book “The Pillar and Affirmation of Truth” (1914) Father P. Florenskii implicitly meant the idea of paraconsistency. Gleam paraconsistency ideas may be detected in the works of A.I.Vvedenskii and N.O.Losskii (1909 - 1917), but the true history of paraconsistent logic emerged due to construction of imaginary logic by N.A.Vasiliev (1910 - 1914). 2. What vague and barely formulated analogies fed Vasiliev's pioneer work? They are: C.S.Peirce's logic of relatives; the symbolist poetry that paid a great deal of attention to the subject of another worlds; special psychological standpoint, used for the critical analysis of Aristotelian logic; Ch.Darwin's ideas on the evolution of life; the analogy with non-Euclidean geometry construction method. 3. Intellectual climate prior to Vasiliev’s works supposed only the abstract possibility of non-Aristotelian logic, the notion of which related to the analogy of non-Euclidean geometry. He even claimed that imaginary logic is constructed by Lobachevskii geometry method. 4. In his imaginary logic Vasiliev discarded fundamental law of Aristotelian logic - the law of contradiction and proposed system free of this law. He argued that the law of excluded middle ought to be completely removed from the “canons of the laws of thought” as well. Nevertheless, in any logic there are laws enabling the reasoning. The minimum of such laws constitute a metalogic - the science of structures valid for every logical system. 5. In early 1920 the phenomenon of ideologized science emerged in the USSR which has negative impact upon Soviet science. Nevertheless, this phenomenon induced original by-product in logic. I.E.Orlov shared orthodox Marxist standpoint and pursued strict dialectical style reasoning. He has goal to construct dialectical logic for natural sciences development that would coincide with the theory of knowledge and objective dialectics. All his numerous philosophical works are done in Hegel’s tradition full of critique of bourgeois ideology. These papers were published in leading Soviet Marxist journals. The only paper devoid of any Marxist (and philosophical) content “The calculus of Propositional Consistency” was published in 1928 in one of Soviet mathematical journals. In this paper Orlov attempted to overcome the paradox of material implication and to move from the “logic of extent” to the “logic of content”. This paper happened to opened modern relevant and substructural logics, and anticipated O.Becker’s 1930 and K.Godel’s 1933 papers for it contained construction of S4 system. Work partly supported by RBRF grant.