Due to the proliferation of electronic commerce and the development of Internet technologies, many firms have considered new pricing-inventory models. In this paper, we study the role of stockless (i.e., zero-inventory) operations in online retailing by a considering duopoly competition in which two retailers compete to maximize profit by jointly optimizing their pricing and inventory decisions. In our model, the retailers are allowed to choose either an in-stock policy or stockless operations with a discounted price. We first present the characteristics and properties of the equilibrium. We then demonstrate that the traditional outcome of asymmetric Bertrand competition is observed under head-to-head competition. However, when the two firms choose different operational policies, with corresponding optimal pricing, they can share the market under certain conditions. Finally, we report interesting observations on the interaction between pricing and inventory decisions obtained from an extensive computational study.