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Current implementations of agent-based online auction systems only support simple predefined bidding strategies for bidding agents. In this paper, we introduce a formal bidding strategy model for specification of flexible and complex bidding strategies. The formal model is defined as a layered bidding strategy model (LBSM), which can be represented using notations borrowed from UML activity diagrams. To support real-time and efficient reasoning, the formal model is converted into a rule-based bidding strategy model (RBSM) specified in bidding strategy language (BSL) that can be directly executed by a reasoning module of a bidding agent. We present an algorithm for converting an LBSM to an RBSM, and an algorithm to drive the reasoning engine. Finally, we develop a prototype agent-based online auction system using JADE, and illustrate how flexible and complex bidding strategies can be precisely specified and efficiently executed.