Polymers exhibit a wide range of behaviors for their dynamics depending on the scale of observation. Lot of efforts has been devoted to this study of several time- and length scales. A particularly suited technique to address this question is NMR relaxation dispersion since probing the dependence of NMR relaxation with Larmor frequency gives access to the molecular dynamics on the corresponding time scale. With specific instruments and methods at least three orders of magnitude can be probed and with the interplay of temperature all the polymer dynamical behaviors can be captured. However so far little has been done with this method to study the behavior of charged polymers, polyelectrolytes, yet they are ubiquitous systems in biological, food or environmental applications, to say the least. We propose here to apply a panel of NMR relaxation methods to investigate changes in polyelectrolyte solutions. We have recently used this approach successfully to understand multiscale water dynamics in the vicinity of proteins or the change of ion transport mechanisms in ionic liquids. For polyelectrolyte solutions, preliminary results obtained in the framework of an international collaboration are promising and show a significant change of the relaxation with the modification of the charge with pH or its screening with salt. The first aim of this project is to assess this phenomenon on a simple system in order to identify the governing parameters for a relevant modeling.