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This paper explores the impacts of absorptive capacity on the behavior of innovating firms competing in a dynamic patent race. We introduce spillovers and absorptive capacities in the Fudenberg, Gilbert, Stiglitz and Tirole patent race with memory. First, we show that incorporating absorptive capacity has different effects according as the firm leads or follows in the race. While the leader is getting soft, the follower revives, allowing him to possibly catch up with the leader. Second, we find that spillovers with absorptive capacities tend to increase the pace of innovation, a somewhat paradoxical outcome.