Abstract : While the superdeformation phenomenon has been observed many times in different mass regions, the excitation energy and angular momentum are not known for most of the superdeformed bands, mainly in the A ~ 150 mass region. We have thus undertaken the search for and study of linking transitions between super- and normal deformed potential wells in the 151Tb nucleus with the EUROBALL IV spectrometer based at the Institut de Recherches Subatomiques de Strasbourg. This nucleus presents the peculiarity of having an excited superdeformed band identical to the yrast one of 152Dy, which has recently been linked to normal deformed states. As the 152Dy nucleus exhibits a shape coexistence in the first potential well, we have also searched for collective rotational bands with prolate but moderate shape, coexisting with the oblate structure of 151Tb. The discovery of new superdeformed bands in the 151,152Tb isotopes, the extension to lower and higher spins of the previously known bands, and mean field calculations with a deformed Woods-Saxon potential have contributed to improve our knowledge as well as raise new questions on the orbitals configuration assignments of these bands.