The world of medicinal therapies has been historically, and remains to be, dominated by the use of elegant organic molecular structures. Now, a novel medical treatment is emerging based on CeO nano-crystals that are discrete clusters of a few hundred atoms. This development is generating a great deal of exciting and promising research activity, as evidenced by this Special Issue of . In this paper, we provide both a steady-state and time-dependent mathematical description of a sequence of reactions: superoxide generation, superoxide dismutase, and hydrogen peroxide catalase and ceria regeneration. This sequence describes the reactive oxygen species (ROS); superoxide, O, molecular oxygen, O, hydroxide ion OH and hydrogen peroxide, HO, interacting with the Ce and Ce surface cations of nanoparticle ceria, CeO. Particular emphasis is placed on the predicted time-dependent role of the Ce/Ce ratio within the crystal. The net reaction is succinctly described as: HO + 2O + 2H → 2HO + 2O. The chemical equations and mathematical treatment appears to align well with several critical in vivo observations such as; direct and specific superoxide dismutase (SOD), ROS control, catalytic regeneration, ceria self-regulation and self-limiting behavior. However, in contrast to experimental observations, the model predicts that the 4+ ceric ion state is the key SOD agent. Future work is suggested based on these calculations.