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We demonstrate experimentally that it is possible to control optically the group velocity of an optical pulse as it travels along an optical fiber. To achieve this control we use the effect of Stimulated Brillouin Scattering. In our experiments we have achieved changes in the group index of 10~3 in several kilometer-length fibers, thus leading to pulse delaying and advancement in the range of tens of nanoseconds. We believe that this is the first evidence of such optically-controlled strong delay changes in optical fibers. In this paper we derive the basic theory behind these group-delay changes and we demonstrate the effect in two kinds of fibers which are conventionally used. © 2004 Optical Society of America.