This chapter presents a possible direction for next-generation immunity-based systems. First-generation immunity-based systems extracted principles for information processing from the immune system and extended them to the framework of the information systems. Immunity-based systems for the next generation would further extend the first generation by assuming not only the principles but also the materials on which the immune systems are based. Antibody-based computation is one candidate for such a direction. A primitive form of arrayed antibodies is shown to demonstrate a level of computational capability comparable to DNA-based computing. The stable marriage problem is used as an illustrative problem for demonstrating antibody-based computing.