A sulfonated aromatic polymer comprising the repeating structural unit of the formula I

—O—Ar¹(SO₃R)_n—C(CF₃)₂—Ar¹(SO₃R)_n—O—Ar²—(X—Ar²)_m—,   (I)

in which Ar¹ and Ar² are, independently of one another, divalent aromatic or heteroaromatic radicals which are optionally substituted by one or more monovalent organic groups which are inert under the conditions of use, R is hydrogen, an alkali metal or alkaline earth metal ion or an ammonium ion, n is an integer from 0 to 3, m is 0, 1 or 2 and X is a —CO—, —O—, —C_pH_2p—, —C_pF_2p— or —S— group, in which p is an integer from 1 to 10, is described. Membranes with high proton conductivities can be produced from this polymer and are preferably used in fuel cells.