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We demonstrate a novel design for a passive all-optical R-S flip-flop with separate set-rest ports based on nonlinearity in the fiber Bragg gratings (FBGs). The spectrum of FBGs in the presence of the Kerr effect is investigated, and cw and transient characteristics of nonlinear-induced bistability of the passive distributed feedback structures are studied by numerical solving of coupled-mode equations. It is shown that a pulse with a pulsewidth of 0.15 ns can switch the state of the flip-flop.