An alkali- and/or alkaline earth-ion sulfur battery having at least one cathode containing a cathode current collector foil, optionally a conductive adhesive interlayer, a primary cathode mass layer containing a conductive dimensionally stable porous host structure, sulfur as an active material, preferably at least 20% of the sulfur present is monoclinic sulfur allotrope, and optionally conductive additives, binders and pore-forming additives; a secondary cathode mass layer containing sulfur and alkali-ion- and/or alkaline earth-ion-intercalating material, optionally a layer containing graphene oxide and/or reduced graphene oxide, heteroatom Group VIIa and/or Group Va elements co-doped graphene, and a Group VIIa and/or Group Va heteroatom-containing polymer; at least one anode and at least one separator. The resulting cells offer a wide range of economic and ecological advantages over the currently available cells, as well as allowing versatility of materials and production processes.