This thesis is aimed at the study of high angular momentum states in neutron deficient nuclei in the mass 60 region, with approximately equal numbers of protons and neutrons, (N~Z). The main motivations of this work are to provide an insight into the mechanisms for generation of high angular momentum states in a limited particle valence space above the N=Z=28 doubly magic core, and to investigate the role of the isospin quantum number in heavy N=Z nuclei. The decay scheme for the odd-odd N=Z nucleus 6231Ga has been deduced for the first time, and the decay schemes for 61Zn and 61Cu have been extended. The data came from two experiments, the first using the reaction 24Mg + 40Ca at a beam energy of 65 MeV, performed at the Argonne National Laboratory, Chicago, US, using the germanium gamma-ray detector array 'AYEBALL' in conjunction with the Argonne Fragment Mass Analyzer and a gas filled ionisation chamber. The second experiment using the reaction 28Si + 40Ca at a beam energy of 88 MeV was performed at the Niels Bohr Institute, Riso, Copenhagen, Denmark using the 'PEX' gamma-ray detector array with a charged particle detector ball and an array of liquid scintillator neutron detectors. The data analysis techniques and results of the experimental analysis are presented. Gamma-ray energy spectra for different nuclei are shown according to the mass, neutron number and proton number of the nucleus. The proposed decay schemes are justified by coincidence and DCO arguments, and are compared to shell model calculations using a restricted pf5/2 g9/2basis. In the case of 62Ga, these are then compared with the latest IBM-4 calculation, which explicitly includes T=0 and T=1 bosons. Suggestions are also made for future work to complement this data.