[en] A short summary is given of the shape changes in nuclei and of the transition from the superfluid to the normal state at high angular momentum. The second part of the paper deals with the theory of transitional nuclei and a brief review of earlier work is given. The method described here consists of solving the Schroedinger equation for a collective Hamiltonian; the potential energy is obtained by taking the liquid-drop energy of an ellipsoidal droplet and then adding to it the shell- and pairing corrections. The collective kinetic energy is usually computed by taking for the rotational part the cranking model expression for the moment of inertia, including the pairing effects, and for the vibrational part an expression for the mass parameter resembling the cranking formula. A derivation of the mass parameter, based on the time-dependent Hartree-Fock theory is given. The resulting equations lead to a cranking-type expression when terms containing the two-body interactions are neglected. A critical discussion of the method of the collective Hamiltonian is finally given; it is based on the generator co-ordinate formalism. (author)