The article refutes the generally accepted belief that Hegel's system had made the most considerable influence on Russian philosophy of the 19th and 20th centuries and argues that in fact the Fichte's late religious philosophy had been more significant. The analysis of the M. Bakunin's anarchism makes it possible to assert that his conception has nothing to do with nihilism and appeared under the enormous influence of Fichte's doctrine. According to Bakunin's conception, the possibility to establish a social structure without state stems from a specific understanding of man and his destiny in the world. Like Fichte, Bakunin thinks that true Christianity gives correct understanding of man which is different from historical Christianity and is based on the principle of the identity of God and man. In accordance with the true Christianity, every man's destiny consists in revealing God with all possible plenitude, while Jesus Christ serves here as a model of the person who has already achieved this aim. This is the fact which determines the rejection of state in Bakunin's conception: as long as people are imperfect, the only way to achieve unity and harmony is external coercion, but those who reveal God within themselves will become perfect and their social life, being based on love and internal freedom, will immediately acquire harmonious form. The article demonstrates that even in his late years, when Bakunin maintained a materialistic worldview, he retained this understanding derived from Fichte's philosophy. It is shown that a close conception of man and society can be found in the views of many other Russian thinkers, in particular, in the F. Dostoevsky's and L. Tolstoy's worldview.