The NF-kappaB regulatory network controls innate immune response by transducing variety of pathogen-derived and cytokine stimuli into well defined single-cell gene regulatory events.We analyze the network by means of the model combining a deterministic description for molecular species with large cellular concentrations with two classes of stochastic switches: cell-surface receptor activation by TNFalpha ligand, and IkappaBalpha and A20 genes activation by NF-kappaB molecules. Both stochastic switches are associated with amplification pathways capable of translating single molecular events into tens of thousands of synthesized or degraded proteins. Here, we show that at a low TNFalpha dose only a fraction of cells are activated, but in these activated cells the amplification mechanisms assure that the amplitude of NF-kappaB nuclear translocation remains above a threshold. Similarly, the lower nuclear NF-kappaB concentration only reduces the probability of gene activation, but does not reduce gene expression of those responding.These two effects provide a particular stochastic robustness in cell regulation, allowing cells to respond differently to the same stimuli, but causing their individual responses to be unequivocal. Both effects are likely to be crucial in the early immune response: Diversity in cell responses causes that the tissue defense is harder to overcome by relatively simple programs coded in viruses and other pathogens. The more focused single-cell responses help cells to choose their individual fates such as apoptosis or proliferation. The model supports the hypothesis that binding of single TNFalpha ligands is sufficient to induce massive NF-kappaB translocation and activation of NF-kappaB dependent genes.