Auction methods, auction systems and servers which can satisfy requirements other than the price for a client are provided. An auction client selects a desired one from time slide schemes from a terminal, and enters a due date in an associated entry field. For example, a due date advance scheme is a scheme in which a person who offers the soonest possible trading date from a due date is determined as a successful bidder. Also, specific details (paying-in, delivery and so on) on the trading date for a payment or delivery of an article, requested to a partner, are specified. These bid condition data are transmitted to the server through a network, and the server collects participants in a bid on a home page. The server receives trading dates offered from terminals of participants, and determines a participant who offers the trading date that most satisfies the trade due date condition offered by the client as a successful bidder.