Absolute concentration robustness is a property that allows signaling networks to sustain a consistent output in the face of protein concentration variability from cell to cell.  This property is structural and can be determined from the topology of the network alone.  In this talk, I discuss this concept first for deterministic systems, and then set out to describe their stochastic behavior.  In the long term, the corresponding stochastic processes undergo an extinction event that eliminates the robustness. However, these systems have a transiently robust behavior that may be sufficient to carry out the necessary signal transduction in cells.  This work has been recently funded by NSF and graduate students are invited to inquire about working with me on this topic.