Biological signaling systems produce an output, such as the level of a phosphorylated protein, in response to defined input signals. The output level as a function of the input level is called the system's input-output relation. One may ask whether this input-output relation is sensitive to changes in the concentrations of the system's components, such as proteins and ATP. Because component concentrations often vary from cell to cell, it might be expected that the input-output relation will likewise vary. If this is the case, different cells exposed to the same input signal will display different outputs. Such variability can be deleterious in systems where survival depends on accurate match of output to input. Here we suggest a mechanism that can provide input-output robustness, that is, an input-output relation that does not depend on variations in the concentrations of any of the system's components. The mechanism is based on certain bacterial signaling systems. It explains how specific molecular details can work together to provide robustness. Moreover, it suggests an approach that can help identify a wide family of nonequilibrium mechanisms that potentially have robust input-output relations.