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Biological regulatory systems have the potential to provide graded responses to stimuli or may demonstrate switch-like properties. Our understanding of the system design principles controlling these responses is still at a rudimentary stage, and here we consider several recent experimental and theoretical studies that focus on these system design principles. Overt positive feedback loops, or double-negative feedback loops, can produce bistable or multistable systems under the appropriate conditions and can produce graded responses under other conditions. Several design features favor bistability in negatively controlled genetic systems, including a high kinetic order for repression and a large difference in the rates of gene expression in the "on" and "off" states. In positive feedback, a high kinetic order for the activation of gene expression favors bistability. Multistability can result from the combined effects of positive and negative regulators, or from the combined effects of regulators that each demonstrate bistability. Finally, bistability can result in enzymatic systems in which multiple reversible covalent modifications occur, even when no overt feedback loops are present.