The aim of our study was the conclusion of the simple kinetic equations to describe ab initio the initiated non-branched-chain processes of saturated free radical addition to C=C, C=O, and O=O bonds of molecules in the binary systems of saturated and unsaturated components. In the processes of this kind the formation rate of the molecular addition products (1:1 adducts) as a function of concentration of the unsaturated component has a maximum. Five reaction schemes are suggested for addition processes of free radicals to the multiple bonds of molecules. The schemes include reactions competing with chain propagation through a reactive free radical. The chain evolution stage in these schemes involves three or four types of free radicals, of which one is relatively low-reactive and inhibits the chain process by shortening of the kinetic chain length. Based on the suggested schemes, nine rate equations containing one to three parameters to be determined directly are set up using quasi-steady-state treatment. These equations provide good fits for the non-monotonic (peaking) dependences of the formation rates of the molecular 1:1 adducts on the concentration of the unsaturated component in liquid homogeneous binary systems consisting of a saturated component (hydrocarbon, alcohol, etc.) and an unsaturated component (olefin, allyl alcohol, formaldehyde, or dioxygen). The unsaturated compound in these systems is both a reactant and an autoinhibitor generating low-reactive free radicals such as СН 2 =С(СН 3 )ĊН 2 , СН 2 =СНĊНОН, НĊ=O, o-СН 3 С 6 Н 4 СН 2 4 O , or 4 HO . A similar kinetic description is applicable to non-branched-chain free-radical hydrogen oxidation. The energetics of the key radical-molecule reactions is considered.