The title polymers have been prepared by nucleophilic substitution of 2,3-dimethyl- and trimethylhydroquinone, and 3,3’-dimethyl- and 3,3’,5,5’-tetramethylbiphenol with difluorobenzophenone. These polymers have been brominated to various degrees of substitution. The dimethyl PEEK can only be monobrominated; trimethyl PEEK yields mono- and dibromomethyl functional groups in the ratio 2:1. These results can be explained by steric hindrance to dibromination of the vicinal methyl groups. Dimethyl- and tetramethylbiphenyl PEEK can be dibrominated completely.