This paper emphasizes the fact that valuable information on the dynamics of high-Tc super-conductors is concealed in that part of the spin-lattice relaxation which arises from quadrupolar interactions. We briefly discuss the problem how to disentangle magnetic and quadrupolar time dependent interactions if both are present, thus leading to multiexponential magnetization recovery laws. We then discuss two examples from our studies of the high-Tc superconductor YBa2Cu4O8 where the identification of a quadrupolar contribution to the spin-lattice relaxation has been es-sential to draw the relevant conclusions. One example is concerned with the charge fluctuations associated with an electronic crossover showing up in the oxygen relaxation. The second example is dealing with the separation of charge and spin excitations and the validity of the single-spin fluid model.