Many products--including microprocessors, telecommunications devices, computer software, and on-line auction services--make use of multiple technologies, each of which is essential to make or sell the product. The owner of one technology benefits from the existence of complementary technologies. We show that, despite this externality, the structure of payoffs that support efficient R&D investment by duopolists racing to discover a single innovation generalizes to the structure that supports efficient investment for complementary innovations. The paper also examines how alternative intellectual property regimes and legal institutions affect R&D investment in complementary technologies. The results have policy implications for the organization of R&D, the assessment of damages for patent infringement, and allocations of value in patent pools.