State-selected differential cross sections (DCSs) have been measured for the OH radicals produced from the reactions of O(P-3) with saturated hydrocarbons by utilizing Doppler-resolved polarization spectroscopy. Stereodynamics in the reactions of secondary (c-C6H12) and tertiary (i-C4H10) hydrogen atoms are discussed based on the dependences of the DCSs on the collision energy and the structure of these hydrocarbons. For the c-C6H12 reaction, the DCS of the OH((2)Pi(3/2),v'=1,j'=3.5,A') shows predominant intensities in the backward hemisphere with reference to the incident O(P-3) atom at a mean collision energy of < E-coll>=12 kJ/mol. When the collision energy is raised to < E-coll>=33 kJ/mol, the OH radicals scattered in the forward hemisphere grow almost to match those in the backward hemisphere. The observed increase in the forward scattering implies that the collision energy makes the large impact parameter collisions contribute to the reactive scattering. At a similar collision energy of < E-coll>=31 kJ/mol the forward scattering component in the DCS of the i-C4H10 reaction does not exceed that of the c-C6H12. This shows that the cone of acceptance is not enlarged in the i-C4H10 reaction from that in the c-C6H12 reaction, as opposed to the expectation based on the height of activation barrier. The absence of the enlargement of the cone of acceptance can be attributed to a large steric hindrance caused by the three bulky methyl groups surrounding the reactive tertiary C-H bond of i-C4H10. The difference in the steric hindrance can explain the difference in the temperature-dependent pre-exponential factors of the macroscopic reaction rates between the abstraction of the secondary and tertiary C-H bonds. The collision energy dependence of the DCS as well as the internal excitation of alkyl radical products reveal that the O(P-3)+alkane reactions are not always dominated by the simple rebound mechanism, which has long been believed.