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We study economies with adverse selection, plus the frictions in competitive search theory. With competitive search, principals post terms of trade (contracts), then agents choose where to apply, and they match bilaterally. Search allows us to analyze the effects of private information on both the intensive and extensive margins (the terms and probability of trade). There always exists a separating equilibrium where each type applies to a different contract. The equilibrium is unique in terms of payoffs. It is not generally efficient. We provide an algorithm for constructing equilibrium. Three applications illustrate the usefulness of the approach, and contrast our results with those in standard contract and search theory.