Description An overview of some methods of parameterizing the amplitudes of two-body interactions will be presented. As an example, the low energy (E < 2GeV) coupled channel pion-pion amplitudes will be used. The main part of the presentation, however, will be the analysis of our most common errors in the parameterization of these amplitudes and their consequences. At the end, the main conditions that should be met by the amplitudes to have the most physical meaning and to be as real as possible will be presented.