We have studied the relaxation of the concentration fluctuations of gelling disk-like clay particles (Laponite) in water containing 5 mM NaCl. At a Laponite concentration of 10 g/l a gel is formed that does not flow when tilted. The comparison of dynamic light scattering and dynamic mechanical measurements shows that the terminal relaxation time of concentration fluctuations diverges not at the gel point, but only when the gel is sufficiently dense to inhibit motion over the length scale on the order of the inverse scattering wave vector. The initial decay of the concentration fluctuations is due to cooperative diffusion and is insensitive to the gel formation. At a concentration of 1 g/L, large aggregates that slowly precipitate are formed. The scattering wave vector dependence of the decay of the concentration fluctuations shows that the aggregates are semi-flexible.