A process for preparing a solution of sulfone-containing tanning materials comprises a) preparing a component A by a1) reacting phenol with concentrated sulfuric acid, with oleum of an SO3 content of from 20 to 65% by weight or with a mixture of sulfuric acid and oleum of an SO3 content of from 20 to 65% by weight, the molar ratio of total sulfuric acid, reckoned as SO3, to phenol being in the range from 0.7:1 to 1.5:1, at from 100 to 180° C. to form a mixture containing phenolsulfonic acid, dihydroxydiphenyl sulfone and sulfuric acid, or mixing the individual components to prepare a corresponding mixture, a2) then condensing said mixture with from 0.25 to 4 mol of urea and with from 0.5 to 4 mol of an aliphatic aldehyde of 1 to 6 carbon atoms per mole of phenol units present at from 40 to 90° C., a3) optionally adding a base to set a pH of from 4 to 5, b) preparing a component B by b1) reacting dihydroxydiphenyl sulfone with from 0.5 to 5 mol of an aliphatic aldehyde of from 1 to 6 carbon atoms and with from 0.4 to 2 mol of sodium sulfite per mole of dihydroxydiphenyl sulfone at from 90 to 180° C., b2) optionally adding an acid to set a pH of from 3.5 to 5.5, c) mixing from 10 to 90% by weight of component A with from 90 to 10% by weight of component B, the sum total of A and B being 100% by weight, and, unless already effected in steps a3) and b2), setting the pH of the mixture to a value in the range from 3.5 to 5.5.