In a process for accelerating the setting and hardening of a material which contains a hydraulic binder or which consists of a hydraulic binder there is used a setting accelerator mixture which is free of alkali metals and free of chlorides. Said setting accelerating mixture contains at least one water soluble sulfate of a polyvalent cation and a further constituent which is selected from the group consisting of calcium aluminate, calcium sulfoaluminate, basic aluminum salts, mixtures thereof or mixtures containing at least one of said constituents and a further component. If the water soluble sulfate of the polyvalent cation is aluminum sulfate, then said compound has to contain crystal water in order to provide the water solubility of said product. With the setting accelerating mixtures, a fast gaining of strength of a corresponding mortar or concrete is achieved and the finally hardened product has better mechanical characteristics then corresponding products prepared without the adding of any set accelerating admixture.