The evidence from both data and models indicates that specific equilibrium climate sensitivity S[X]—the global annual mean surface temperature change (ΔTg) as a response to a change in radiative forcing X (ΔR[X])—is state dependent. Such a state dependency implies that the best fit in the scatterplot of ΔTg versus ΔR[X] is not a linear regression but can be some nonlinear or even nonsmooth function. While for the conventional linear case the slope (gradient) of the regression is correctly interpreted as the specific equilibrium climate sensitivity S[X], the interpretation is not straightforward in the nonlinear case. We here explain how such a state-dependent scatterplot needs to be interpreted and provide a theoretical understanding—or generalization—how to quantify S[X] in the nonlinear case. Finally, from data covering the last 2.1 Myr we show that—due to state dependency—the specific equilibrium climate sensitivity which considers radiative forcing of CO2 and land ice sheet (LI) albedo, S[co2,LI], is larger during interglacial states than during glacial conditions by more than a factor 2.