We study security-bid auctions in which bidders compete for an asset by bidding with securities. That is, they offer payments that are contingent on the realized value of the asset being sold. Such auctions are commonly used, both formally and informally. In formal auctions, the seller generally restricts bids to an ordered set, such as an equity share or royalty rate. By restricting the bids, standard auction formats such as first and second-price auctions can be used. In informal settings with competing buyers, the seller does not commit to a mechanism upfront. Rather, bidders offer securities and the seller chooses the most attractive bid, based on his beliefs, ex-post. We characterize equilibrium payoffs and bidding strategies in both formal and informal auctions. For formal auctions, we examine the impact of both the security design and the auction format. We define a notion of the steepness of a set of securities, and show that steeper securities lead to higher revenues. We also show that the revenue equivalence principle (that expected revenues are independent of the auction format) holds if the set of permissible securities is ordered and convex (such as equity). Otherwise, it need not hold. For example, when bidders offer standard debt securities, a second-price auction is superior. On the other hand, if bidders compete on the conversion ratio of convertible debt, a first-price auction yields higher revenues. We then show that an informal auction yields the lowest possible revenues across all possible formal mechanisms. Finally, we extend our analysis to consider the effects of liquidity constraints, different information assumptions, and some aspects of moral hazard.