In our work we have proposed an agent-based model e-commerce system. In this system buyer agents negotiate prices with seller agents. Thus far our attention was devoted "one sided" price negotiation mechanisms, i.e. mechanisms in which one side is active, while the other side is passive (possibly other than initiating the process). Examples of such negotiations are, among others, English and Dutch Auctions, as well as a number of sealed-bid auctions. Here, we focus our attention on auctions in which both sides take active part. We discuss how these auctions can be incorporated into our system and present their UML formalizations.