Disclosed are a hydraulic binder composition containing at least 50% by weight of ground granulated blast furnace slag and a system for activating the slag, the system containing at least calcium sulphate, at least one product chosen from a source of Portland clinker and lime, at least one aluminum derivative and at least one alkali metal or alkaline earth metal salt; containing a ready-to-mix building material composition comprising such a hydraulic binder and aggregates of inert material capable of being agglomerated in the presence of an aqueous phase; and a process for employing the ready-to-mix composition containing a stage of mixing the said composition with water for the purpose of the preparation of a building material, such as a concrete or mortar, and in particular an adhesive mortar, pointing mortar or levelling mortar or coating.