This paper presents a model of a firm's R&D behavior over an entire product life cycle. Beginning with the search stage, modelled as a patent race, firms raise their R&D expenditures until one firm succeeds with a technological breakthrough in creating a new product market. The following R&D behavior of the successful entrepreneur, devoted to incremental product and process innovations, varies in a characteristic way over the new product's life cycle. Under reasonable conditions, R&D activities rise in the early stages but decline when the market matures. Overall, supply and demand factors combine to determine the R&D time-path.