Abstract: The process for producing high-T.sub.c superconductors containing thallium, calcium, barium and copper, possibly also lead and/or strontium, provides for a thallium-free precursor to be produced in a first reaction step and this to be then mechanically triturated, subsequently heated to temperatures in the range from 700.degree. to 950.degree. C. and heat treated for a period of at least 3 hours. The mixture is then cooled to ambient temperature and ground again. Finally, it is heat treated at temperatures of from 400.degree. to 500.degree. C. in a stream of pure oxygen. The thallium-free precursor is then triturated with Tl.sub.2 O.sub.3, if desired shaped into a shaped part and then oxidatively fired in a flowing gas atmosphere.