This project will study the structure of atomic nuclei at the limits of elongation and stability. Highly elongated, or superdeformed, shapes of nuclei near lead will be studied by measuring magnetic moments of these excitations, studying the decay of these shapes to excitations with normal deformations, and extending the search for these shapes to systems which are highly likely to fission. The structure of nuclei near the region where decay by proton emission can occur will be probed by studying the magnetic moments of the ground states and the excitations built on isomers which decay by emitting a proton or alpha particle. Techniques will be developed for future studies of nuclear magnetic properties of nuclei far from stability produced as radioactive ion beams.