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The formation of a submicron fibrous (SMF) structure in low carbon low alloy steels under severe warm rolling is investigated. It is shown that by varying modes of deformation one can obtain structures with either equilibrium or nonequilibrium grain boundaries (GBs). It is established that SMF structure provides for a sharp increase in strength properties (by a factor of 23) as compared to those of coarse-grained material. An analysis of this effect based on Hall-Patch relation models is given.