A process for recovering tantalum and/or niobium metal compounds from an ore containing one or more compounds of said metal or metals and further containing uranium, thorium, radium, titanium, and rare earth metals, wherein in a first step (I) the crushed ore is decomposed with a 0.5 to 6-fold amount of 70 to 96 percent sulfuric acid at elevated temperatures in the range of 200.degree. to 350.degree. C. for 0.5 to 3 hours with air as the oxidation agent, whereby the elements uranium, thorium and titanium are brought into solution by being converted to water soluble sulfates, the resulting solution being a solution of sulfuric acid comprising 30 to 100 grams H.sub.2 SO.sub.4 per liter, while substantially all the transition metals remain together with radium in a water-insoluble residue, the residue then being decomposed within 6 to 20 hours in a second step (II) by leaching the residue of the first step (I) with a mixture of sulfuric acid and hydrofluoric acid at a temperature in the range of from 80.degree. to 120.degree. C., whereby there results a solution of transition metals wherein HF is between 8 and 30 normal and sulfuric acid is between 25 and 26 normal, and from which, by means of appropriate organic extraction agents, the transition metals are extracted as fluoro-complexes by liquid-liquid extraction, and the individual transition metals are recovered free from radioactive constituents as pure compounds in yields of more than 95 percent of the charge, while the refined products of the liquid-liquid extraction and wash water are further processed to eliminate the last traces of RaSO.sub.4.