The aim of this study was to devise simple kinetic equations to describe ab initio initiated nonbranched-chain processes of addition of saturated free-radical to double bonds of unsaturated molecules in binary reaction systems of saturated and unsaturated components. In these processes the formation rate of the molecular addition products (1:1 adducts) as a function of concentration of the unsaturated component reaches a limiting value. Five reaction schemes are suggested for the addition processes. The proposed schemes include the reaction competing with chain propagation reactions through a reactive free radical. The chain evolution stage in these schemes involves three or four types of free radicals. One of them is relatively low-reactive and inhibits the chain process by shortening of the kinetic chain length. Based on the suggested schemes, nine rate equations are deduced using quasi-steady-state treatment. These equations provide good fits for the non-monotonic (peaking) dependences of the formation rates of the molecular products (1:1 adducts) on the concentration of the unsaturated component in the binary systems. The unsaturated compound in these systems is both a reactant and an autoinhibitor generating low-reactive free radicals. A similar kinetic description is applicable to the nonbranched-chain process of the free-radical hydrogen oxidation, in which the oxygen with the increase of its concentration begins to act as an oxidation autoinhibitor (or an antioxidant). The energetics of the key radical-molecule reactions are considered.