Polyarylene ether sulfones which have a reduced viscosity of 0.1 to 2.0 dl/g, measured at 25.degree. C. in a 1% solution in N-methylpyrrolidone (NMP), and which contain, based on the total number of structural units present in the polyarylene ether sulfone resin, 99-1 mol % of a recurring structural unit of formula I ##STR1## and 1-99 mol % of a recurring structural unit of formula II--O--Ar.sub.2 --O--Ar.sub.1 -- (II)wherein the aromatic rings in the structural unit of formula I are unsubstituted or substituted by one or more C.sub.1 -C.sub.4 alkyl groups, C.sub.1 -C.sub.4 alkoxy groups or halogen atoms, Ar.sub.1 is a radical of formula IIIa-IIIc ##STR2## wherein a is 0 or 1, ##STR3## which radical is unsubstituted or substituted by one or more C.sub.1 -C.sub.4 alkyl groups, C.sub.1 -C.sub.4 alkoxy groups or halogen atoms, and Ar.sub.2 is a radical of formula IVa-IVe ##STR4## wherein b is 0 or 1 ##STR5## wherein c is 0 or 1 ##STR6## wherein Z is --CO--, --SO.sub.2 --, --SO--, --S--, --O--, ##STR7## wherein R is methyl or phenyl, which radical is unsubstituted or substituted by one or more C.sub.1 -C.sub.4 alkyl groups, C.sub.1 -C.sub.4 alkoxy groups or halogen atoms, are soluble in customary organic solvents and can be processed from the solution to films or incorporated in other matrix resins.