[en] The aim of the investigation is to compare; the description of some specific nonrotational states within the following theories: the quasiparticle phonon nuclear, the interacting boson and the Bohr-Mottelson. Special emphasis is given to the quasi-particle-phonon nuclear model and to the multiphonon method. The basic assumptions of the different models are given. Some examples are provided. The various microscopic theories treating properly the Paul principle's effect on nuclear vibrations show that it is not possible to obtain a compressed energy spectrum in realistic calculations. It is suggested to look for specific reactions, which are able to give experimental evidence of the low-lying two-phonon states and to check the accuracy of the different theoretical predictions