Abstract
In recent papers we developed and applied a mode (weak) coupling method for nuclei which show weak anharmonicity. In this work we demonstrate that this approach is rigorously equivalent to Dyson's finite boson expansion which has been generalized for nuclei by Janssen et al. We discuss here in detail the advantages and drawbacks of Dyson's method as for instance the appearance and localization of spurious states due to a violation of the Pauli principle. We also give a very simple prescription for calculating matrix elements in Dyson's method.