This paper briefly reviews an extensive set of studies of the reactions of fluorine atoms with olefins, dienes, aromatic and heterocyclic molecules by the method of crossed molecular beams. From measurements of the angular distribution of products and the recoil energy spectrum of products it is inferred that the statistical theories of reaction are inadequate. Although RRKM theory seems capable of predicting the ratios of cross sections for pairs of products, the same theory is incapable of accounting for the internal energy distribution of the products. The failure of the hypothesis that internal energy exchange is more rapid than chemical reaction is discussed and a proposal advanced to explain the origin of the failure.