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The study of nuclear structure at very high angular momentum requires sensitive detector systems in order to detect weak signals. Large gamma-ray arrays were used in this thesis to study the high-spin states in 166;168;170Ta and 160Yb. These arrays were located at facilities such as: Florida State University (FSU), Argonne National Laboratory (ANL), Lawrence Berkeley National Laboratory (LBNL), and Yale University. A study utilizing the Gammasphere spectrometer (the world's most powerful array) resulted in a dramatic expansion of over 400 new gamma-ray transitions organized into 29 rotational bands in the level scheme of 170Ta. Alignment behavior, an additivity of Routhians analysis, and B(M1)/B(E2) transition strength ratios are used to support the configuration assignments made for this nucleus. The observation of linking transitions between almost all of the bands allowed the relative excitation energies to be determined for nearly the entire level scheme. All of the above work on 170Ta, resulted in the most comprehensive high-spin level scheme in odd-odd nuclei to date. A significant expansion has also been made to the level scheme of 168Ta using the FSU gamma-ray array. An additivity of alignment analysis, along with a B(M1)/B(E2) analysis made it possible to assign band configurations. Although an experiment studying the high-spin structure of 166Ta using the Yale University spectrometer (YRAST Ball) was performed, detailed analysis resulted in the observation of no new information. A new extremely low intensity band structure has also been observed in 160Yb from another Gammasphere experiment. This structure is interpreted as the first observation of a stable triaxial shape in Yb nuclei.