Very exotic shapes can be assumed for the nuclei at high angular momen
ta. Their study has become possible with the advent of the last genera
tion high-resolution gamma-ray spectrometers. In this talk results are
presented on superdeformed nuclei of the A = 140 mass region where a
detailed spectroscopy in the second minimum is now possible. Hyperdefo
rmed rotational bands, expected in the third minimum, lie at even high
er spins where their observation is very difficult from the experiment
al point of view. We have up to now only weak signals of their presenc
e. The status of the search for hyperdeformation in Dy-152 is reported
.