In the context of the disposal of radioactive wastes in a deep, geological, clay repository, concretes having low alkalinity and low heat of hydration referred to as “low-pH concretes” were designed. The degradation of the properties of the clay and the risk of microcracking within a massive concrete body during hydration can be limited using these types of concrete, the specificities of which are the nature of the binder, which was a ternary blend in this study, and the high pozzolanic addition content. The objective of this study is to provide data of long-term behaviour and durability of two low-pH concretes. To this end, an experimental campaign has been led which focuses on the delayed strains, shrinkage and creep, and transfer properties. The results show that these concretes have similar mechanical characteristics to that of classical high-performance concretes, but are distinguished by better transfer properties that make them interesting for confinement structures. These original data will be useful for modelling with a view to predict long-term behaviour and to design special structures with accuracy.