The problems of the spurious (ghost) states and of convergence and stability of the model's solutions are considered as applied to the theories which can be classified as the versions of the extended random phase approximation. It is shown that stability is ensured by making use of the subtraction method proposed previously. The spurious states are eliminated with the help of the projection technique. The particular case of the dipole spurious states is considered. These results are illustrated by the calculations of the low-lying states in the nucleus (208)~Pb.
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