energy for the alpha-cluster DNS are close or even lower than the binding energy for these nuclei [11]. This is also in agreement with the fact that these nuclei are good alpha-emitters. Previously, we considered the mass-asymmetry motion variable as the only intrinsic col- lective coordinate describing DNS. However, the nuclei demonstrate yet another sign of reflection-asymmetry, namely, low-lying (started below 1 MeV) negative parity rotational bands with K =0 which can be related to the non axially-symmetric reflection-asymmetric mode. The natural way to obtain such an excitation in the framework of the dinuclear system model is to consider the relative angular motion of the fragments in the dinuclear systems illustrated in Fig. 1. It is the aim of the present investigation to extend the DNS model to take into account such excitations. Basically, there are two physically different cases which can be distinguished. If the heavy fragment of DNS, whose lighter fragment is an α -particle is strongly deformed, the light fragment is tend to stay near the pole of the heavy cluster performing the small angular oscillations around this position. This case which holds for the heavy actinides is considered in the work []. If the heavy fragment is nearly spherical, the interaction between the frag- ments is small to prevent the light cluster from rolling along the surface of the heavy one. Such a case is realized in the light isotopes of actinides, including the $^{220}$Th considered here. The structure of $^{220}$Th has been analyzed in several theoretical publications [12, 15, 16]. Here, we apply an approach of the dinuclear system model. The degrees of freedom chosen to describe a system with nearly spherical heavy cluster are related to the rotation of the DNS as a whole, to the quadrupole oscillations of the heavy fragment, and to the transfer of nucleons between the fragments. The Hamiltonian of the model can be presented in the form where ˆ H$_{0}$ describes independent fragments of the system and ˆ V$_{int}$ describes the interaction between the fragments. ˆ H = ˆ H$_{0}$ + ˆ V$_{int}$, (1) II. MODEL A. Hamiltonian 4