The work described in this thesis comprises an investigation of the reaction 37Al('),p)26Mg and the reaction 7Li(p/7)8Be*. Measurements were made of the cross-sections for the 27Al(f,p)3 Mg reaction, leading to discrete excitation states of the residual nucleus. These measurements were carried out using a quasi-monochromatic photon beam obtained by the photon tagging technique. Cross-sections are presented for photon energies from 47 to 64 MeV and for nucleon emission angles between 60° to 120°. The general features of the data are: i) angular distributions which are forward peaked, ii) cross-sections which decrease exponentially with photon energy. Comparison with the predictions of the direct knockout model indicate that the (f,p) cross sections may be explicable assuming no other process contributes. A comparison of the results from the present work with those of a recent27 Al(e,e'p)26Mg experiment, indicates that the (f,p) and (e.e'p) reactions excite the same residual states (g.s 0+, 1.81 MeV 2+, 2.94 MeV 2+, 4.35 MeV 2+ and 7.86 Mev) in similar relative proportions and exhibit similar functional dependencies on momentum transfer. The 90° yield was measured for proton capture to the region of the 2+ isospin-mixed pair of levels in 8Be* using the reaction 7Li(p,f)8Be* -> 2a for incident proton energy 25 MeV. The measurements were made at the SERC Nuclear Structure Facility, Daresbury, U.K. Gamma-rays were detected by a 25 cm x 35 cm NaI(Tl) detector and two alpha particles were detected by 50 mm x 50 mm silicon strip detectors. Two alpha particles and f-rays were detected all together in a triple coincidence. This new datum is shown to be more consistent with a resonance type reaction mechanism than the previously proposed direct capture process.