In explosive astrophysical environments such as novae, X-ray bursters and supernovae, conditions of extreme temperature and density are achieved. Under such conditions, both the rate of energy release and path of nucleosynthesis are governed by reactions on unstable nuclei. In this light, direct reaction studies using radioactive ion beams play a vital role in determining nuclear reaction rates. However, in the vast majority of cases, direct measurements are not possible and as such, indirect measurements are equally important for the understanding of the main reaction processes driving astrophysical events. In this thesis work, indirect studies of the astrophysically important 19Ne(p,γ)20Na and 29P(p,γ)30S reactions have been performed. For the first reaction, a β-delayed proton decay study of 20Mg was performed to gain information about the spin-parity assignment of the first key resonance above the proton emission threshold in the compound nucleus 20Na. This resonance is expected to dominate the 19Ne(p,γ)20Na reaction rate in explosive astrophysical environments and its identity has been under discussion for a long time, with J π = 1+ and 3+ assignments suggested. In the present study an upper limit on the β-decay branch to this state of 0.02% with a con dence level of 90% is reported. This is signi cantly more stringent than previous studies and makes a 1+ assignment highly unlikely, favouring instead a 3+ assignment. A 3+ assignment is predicted to have a signi cantly higher resonance strength and produce a proportionately higher 19Ne(p,γ)20Na reaction rate in X-ray burst conditions. The second study performed was a detailed gamma-ray spectroscopy study of the nucleus 30S. Excitation energies have been determined with improved precision over previous studies and the first,firm spin-parity assignments of key 29P + p resonant states, expected to dominate the 29P(p,γ)30S reaction in stellar scenarios, have been made. An evaluation of the 29P(pγ)30S reaction over the temperature range T = 0.06-2.5 GK shows that the 3+ and 2+ resonant states located at Er = 292.0(9) and 413.1(10) keV, respectively, dominate the 29P(p,γ)30S reaction rate in ONe novae, while the 413 keV resonance is expected to govern the rate in X-ray burster environments. These new, precise resonance energy measurements and firm spin-parity assignments have signi cantly reduced uncertainties in the 29P(p,γ)30S reaction in ONe novae and X-ray bursters. In particular, the reaction rate is now speci ed precisely enough for calculations of isotopic abundances in ONe novae ejecta.