This work presents experimental results about the saturation of bentonite under constant volume and the simultaneous development of swelling pressure. The tests have been performed at room temperature under conditions of free availability of liquid water. Water intake and swelling pressure development were measured. The tests have been performed with a bentonite compacted to dry densities between 1.4 and 1.7 g/cm3. The results obtained show that swelling pressure does not develop in a uniform way, but present more that one swelling stage. After a sharp initial increase, there is a period of time in which pressure increases more slowly or—for the lower densities—even decreases. This behaviour has also been detected in other clays and can be explained as a consequence of the complex fabric of this material, with the typical double porosity observed in expansive clays. A double structure framework specifically developed to analyse the behaviour of swelling clays has been used in this work to model the swelling pressure evolution of the FEBEX bentonite.