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The mitochondrial F-ATPases make about 90% of cellular ATP. They are multi-protein assemblies with a membrane extrinsic catalytic domain attached to a membrane embedded sector. They operate by a mechanical rotary mechanism powered by an electro-chemical gradient, generated across the inner mitochondrial membrane by respiration. A detailed molecular description has been provided by X-ray crystallographic studies and "single molecule" observations of the mechanism of the F1 catalytic domain. Details are known also of the architecture of the peripheral stalk of part of the stator and the membrane embedded region of the rotor. However, knowledge of the detailed structure of the rest of the membrane domain, and the detailed mechanism of generation of rotation is lacking. Recently, studies of the intact mitochondrial F-ATPases, determined by cryo-electron microscopy (cryo-em), have provided structural information at intermediate levels of resolution. Whilst these structures have given insights into the mechanism of generation of rotation, the information required for a molecular understanding of this mechanism is still lacking. Moreover, the locations and roles of six supernumerary membrane subunits are unclear. Some of them are likely to be involved in the formation of dimers of the enzyme which line the edges of mitochondrial cristae. Therefore, in this thesis, a procedure is described for the purification of dimers of the bovine and yeast F-ATPases. The structure of the bovine dimer has been determined by cryo-em at a resolution of ca. 6.9 Angstrom. This structure confirms features concerning the trans-membrane spans of the a-, A6L- and b-subunits observed in the monomeric complex. In addition, the single trans-membrane a-helix of the f-subunit has been located, and the subunit appears to mediate dimer formation. The structure of A6L has been extended, and the a-helices of subunits e- and g- have been located. Another novel feature has been assigned to the DAPIT subunit, and may provide links between dimers in forming larger oligomers. Further improvement in the resolution of the structure is hampered by the extreme conformational heterogeneity of the F-ATPase. To this end, the simpler Fo membrane domain has been isolated and characterized initially by electron microscopy in negative stain.