The present disclosure provides methods for modifying and cross-linking polybenzimidazoles, PBI. In one embodiment, the polybenzimidazole reacts with a compound, which has a halogen and a double bond functionality and which comprises a halogen and an organic group to form modified polymers by means of a nucleophilic substitution of the amine proton of the benzimidazole functionality in a solution, and a functional group is connected via each resulting free double bond and/or the polymers that are thus modified are cross-linked.