To obtain a crosslinked aromatic polymer which is useful as an interlayer dielectric material and exhibits an excellent heat stability and low permittivity and moisture absorption by heating an aromatic polymer having bonded grafts to a specified temperature in an inert atmosphere to thermally crosslink the polymer.

An aromatic polymer having grafts represented by formula I and/or formula II is crosslinked by heating at 200-450°C in an inert atmosphere. In the formulas, R1 to R4 are each H or 1-8C alkoxy. Preferably, the aromatic polymer is selected from among aromatic polysulfones, aromatic polyimides, aromatic polyamides, aromatic polyqunolines, and poly(arylene ether) polymers and the crosslinking is conducted at 300-450°C. The objective graft aromatic polymer can be prepared e.g. by bringing a poly(arylene ether) polymer [e.g. a polymer represented by formula III (wherein x is about 5-10,000)] into contact with a tert, alkyl lithium at -40 to -10°C in a suitable solvent followed by the addition of a ketone (e.g. a compound represented by formula IV or V) at -10 to 25°C.