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This paper presents a logic-program-based mechanism of negotiation between two agents. In this mechanism an extended logic program (ELP) is regarded as an agent. The negotiation process between two agents is then modelled as multiple encounters between two ELPs, each of which selects an answer set as its initial demand. Both agents mutually revise the original sets of demands through accepting part of the opponent’s demand and/or giving up part of its own demand. The overall dynamics can be regarded as mutual updates between two extended logic programs. A deal to achieve an appropriate negotiation solution is put forward. The conditions of existence and terminability of an appropriate negotiation are given. Properties of a negotiation solution are discussed, including its weak Pareto optimality.