Abstract: The invention concerns a process for the preparation of a hardening accelerator composition by reaction of a water-soluble calcium compound with a water-soluble silicate compound and by reaction of a calcium compound with a silicon dioxide containing component under alkaline conditions, in both cases the reaction being carried out in the presence of an aqueous solution of a water-soluble polymer, which contains sulphonic acid and/or sulphonate groups and aromatic groups. The invention concerns also the reaction product of said processes and its use as hardening accelerator for building materials.