A method of producing a cross-linked polyacrylonitrile-sulfur composite material, in which polyacrylonitrile is reacted with sulfur and at least one cross-linking agent to form a cross-linked polyacrylonitrile-sulfur composite material and the cross-linking agent includes at least one functional group, selected independently of one another from an ethylenically unsaturated functional group, an epoxy group and a thiirane group. In addition, the invention relates to a polyacrylonitrile-sulfur composite material, a cathode material, an alkali metal-sulfur cell or an alkali metal-sulfur battery as well as to an energy store.