Models of collusive bidder behavior at single-object second-price and English auctions are provided. The ind ependent private values model is generalized to permit the formulatio n of coalitions and a strategic response by the auctioneer. Cooperati ve strategies are found to be dominant in these models; coalitions of any size are viable, and the payoff to each member increases with th e size of the coalition. In addition, the collusive strategies of the coalition represent a noncooperative equilibrium. The optimal respon se of the auctioneer is to establish a reserve price that is a functi on of the coalition's size. These and other features of the model are found to be consistent with the essential features of actual behavio r.