The discovery of crude oils and condensates at ever higher temperatures casts doubt on the validity of the usual geochemical modelling approach, that uses empirical reactions and rate constants. The solution used to account for such a high thermal stability is presently to adjust the rate parameters, but the physical meaning and scientific value of such a strategy can be questioned. We have developed a mechanistic model consisting of 5200 lumped free radical reactions to describe the thermal evolution of a mixture of 52 organic species meant to represent light petroleum. Rate constants used are those available in the literature or estimated using well established thermochemistry-reactivity correlations. Chemical structures included in the model are linear, branched and cyclic hydrocarbons, hydro-and alkyl-aromatics, PAHs, and three heteroatomic compounds. Reactions include cracking and alkylation chains and inhibiting and accelerating reactions from the various reactants. This model has been applied to several mixtures with various proportions of reaction inhibitors and accelerators, and to a composition representing a light mature oil. From the results obtained, we conclude that mature oils will be stable up to 240-260 C, depending on their composition, and that the thermal cracking of oil to gas is not possible under reasonable basin conditions. The kinetics of petroleum cracking are thus much slower than generally recognized.