The NF-kappaB signaling system is involved in a variety of cellular processes including immune response, inflammation, and apoptosis. Recent experiments have found oscillations in the nuclear-cytoplasmic translocation of the NF-kappaB transcription factor [Hoffmann, A., et al. (2002) Science 298, ; Nelson, D. E., et al. (2004) Science 306, .] How the cell uses the oscillations to differentiate input conditions and send specific signals to downstream genes is an open problem. We shed light on this issue by examining the small core network driving the oscillations, which we show is designed to produce periodic spikes in nuclear NF-kappaB concentration. The presence of oscillations is extremely robust to variation of parameters, depending mainly on the saturation of the active degradation rate of IkappaB, an inhibitor of NF-kappaB. The oscillations can be used to regulate downstream genes in a variety of ways. In particular, we show that genes to whose operator sites NF-kappaB binds and dissociates fast can respond very sensitively to changes in the input signal, with effective Hill coefficients of >20.