A systematic occurrence of the super‐ and hyper‐deformed nuclear configurations is illustrated for 58≤Z≤92 nuclei. The cases selected correspond to the most stable among those exotic configurations. Here we arbitrarily qualify the configurations as ‘‘reasonably stable’’ if the corresponding minima on the total energy surfaces are surrounded by the potential barriers of at least 1000 keV. (Most of the interesting cases correspond to much higher barriers). The strongest effects predicted correspond to ⋅Z∼(76–84) nuclei where the hyper‐deformation at both low and high spins seems to be a ‘‘usual situation’’.