The work in this thesis investigates the selectivity in the direction of attack in the chlorination of a wide variety of substituted alkanes. The main chlorinating agent studied is atomic chlorine, although the selectivity of some other hydrogen abstracting radicals receives attention. Gas phase chlorination is studied, but more attention is given to the effect of solvent systems on the reaction selectivity. The chlorination of 1,1-dichloroethane is studied. The relative Arrhenius parameters for the gas phase reaction as well as for the reaction in non-complexing and complexing liquid phase systems are determined. The reaction selectivity is shown to be a balance of enthalpy and entropy effects. The selectivity in a range of solvent systems is investigated. The novel use of perfluorinated compounds as solvents is studied and selectivities are found to be nearly as high as those in the gas phase. Earlier work on the directive effects in the chlorination of 1-substituted butanes in the gas phase is extended to both non-complexing and complexing liquid phase media. The results agree with earlier proposals that in the liquid phase the inductive effect of a substituent influences the reactivity of the carbon centres much further along the alkane chain than in the gas phase. They also indicate that in complexing media the deactivating effect of the substituent is diminished and higher selectivities are obtained. The chlorination and bromination of 1-nitrobutane is studied. This is one of the few studies that have been made on the halogenation of nitroalkanes. The electron withdrawing power of the nitro group makes it the strongest deactivating group so far observed. For the first time the directive effect of two substituents, one at each end of an alkane chain, is studied. The chlorination of 1,4-disubstituted butanes are investigated. The results go some way to confirm that the polar inductive effect of a substituent is diminished in complexing media. They also confirm that in non-complexing media the effect of the substituent is felt along the whole butane chain. The gas phase results indicate that the presently held theory that in gas phase chlorination the substituent only affects the reactivity of the two carbon centres adjacent to it may not now be wholly acceptable.