This thesis is concerned with the study of the spin-dependence of low-energy deuteron stripping on light and heavy target nuclei. In the case of a heavy target, the relative importance of the folding model spin-orbit interaction and (d,p) channel coupling effects upon the elastic vector analyzing power for deuteron scattering from [90]Zr at 5.5 MeV is studied. Coupled channels calculations areperformed in which the elastic channel and neutron transfer to thestrongly populated states of [91]Zr are treated explicitly. The resultsof these calculations indicate significant corrections to the elastic iT[11] and (d,p) reaction observables and provide a consistentqualitative description of the data. In case of a light target nucleus, it has been suggested that the spin degree of freedom in plasma fusion reactions could be utilised toenhance or suppress fusion reaction rates. For example if the d(d,n)3He reaction were suppressed then a 'neutron-free' d-3He fusion reactor is likely to work. This suppression is thought to occur at lowenergies when the deuterons are polarized with spin parallel. Calculations by Hofmann and Fick showed that the d-d reaction initiatedby low energy polarized deuterons is not suppressed and hence neitheris the neutron production. These results were contradicted by Zhang etal. In order to throw further light on the question an approximate RGM3calculation has been formulated in which the role of D-states of 3He and the deuteron were studied. In these calculations the initial state is described by distorted wave generated by i) non-local separable potentials, and ii) the orthogonality condition model (OCM). In each case the d-d phase shifts from the RGM were fitted. Nuclear wave functions consistent with a realistic nucleon-nucleon interaction wereused throughout. The distorted wave in the exit channel has been generated by a local neutron optical potential which fits the n-3He scattering data. In marked contrast with the previously reported DWBA calculations,which claim to reproduce the data, it is found that the data isoverestimated by a factor of 150 at a centre of mass energy at 55 KeV.Repeating the calculations using another neutron optical potential,which also fits the n-3He scattering data, yields a good agreement with the data.