Kinetic demixing in quaternary mixed oxides has not been investigated previously, either theoretically or experimentally. In this theoretical study, we derive simple and exact analytical expressions that describe the steady-state cation concentration profiles resulting from kinetic demixing in mixed oxides of the O type. The concentration profiles are expressed in terms of cation-vacancy exchange frequency ratios. We assume a random distribution of cations and make use of the Moleko-Allnatt exact sum-rule expression relating the phenomenological coefficients in the ternary random alloy (...) to the vacancy mechanism operative. We employ Monte Carlo simulation of kinetic demixing to verify the result of the analysis. We discuss how kinetic demixing profiles can be processed to obtain atom-vacancy exchange frequency ratios. We also discuss how atom-vacancy exchange frequencies themselves might be obtained from available diffusivities in the quaternary oxide. (shrink)