This work focuses on the creep of clay-based materials, which exhibit significant analogies with cement-based materials. Here, we studied the creep of clay at two scales and with two techniques: numerically (with molecular simulations) at the scale of a clay layer (nm), and experimentally at the scale of thin self-standing clay films (few dozen μm). At the scale of the clay layer, numerical simulations showed that the shear rate was constant over time and an affine function of the shear stress. Creep experiments showed that, after a transient period, the creep function of our thin self-standing clay films was a logarithmic function of time. A comparison of the results obtained at the two scales shows that the origin of the logarithmic feature of clay creep must at least partly originate from a scale greater than that of an individual clay layer. By analogy, such result is likely to hold for cementitious materials, which are also known to creep logarithmically with respect to time in the long term: the origin of this logarithmic feature is likely to stem at least partly from a scale greater than the scale of an individual C-S-H layer.