An investigation of the electronic structure of some transition metal clusters comprising anti-ferromagnetically coupled, heterometallic arrays of eight metal ions that are wheel-shaped, is reported.The compounds were synthesized and provided by Dr. Grigore Timco of The University of Manchester and are formulated by their metal content as Cr7M, where M = a divalent 3d metal. Two families of wheels are the subject of this research, defined 'green' and 'purple' from their physical appearance. Within each family, the compounds are all isostructural.From simulation using a single Hamiltonian for Cr7M-purple compounds, where M = Zn, Mn, or Ni, it is shown that with only two exchange parameters, one JCr-Cr and one JCr-M, data from bulk magnetization, neutron scattering, Electron Paramagnetic Resonance (EPR) spectroscopy at multiple frequencies and specific heat measurements can be modelled and that there is transferability of parameters. Preliminary attempts to measure electron spin relaxation times for two of the purple wheels have shown values of T1 and T2 that are comparable with those of the more extensively studied green wheels and hence further studies in this area are warranted.Variable temperature Q- and W-band EPR spectra for a series of nine heterodimers comprising one green and one purple wheel, M=Zn, Mn or Ni in each case, are reported. For Cr7Zn-purple there is no magnetic exchange detected, whereas weak and quantifiable exchange is required to interpret the spectra from the other six dimers.EPR studies of three trimers of the form purple-green-purple are reported and the presence of magnetic exchange is identified by comparison with the spectra of the component single and double wheel compounds, although this is not quantified because of the numerical size of the simulations that are required. The process of comparing simulated to experimental spectra is a complex problem and one which is central to the work reported in this thesis. The problem of fitting has been investigated and two novel solutions, one based upon pixel mapping and the other based on wavelet transformation are proposed.