Increasingly, many systems are being conceptualized, designed, and implemented as marketplaces in which autonomous software entities (agents) trade services. These services can be commodities in e-commerce applications or data and knowledge services in information economies. In many of these cases, there are both multiple agents that are looking to procure services and multiple agents that are looking to sell services at any one time. Such marketplaces are termed continuous double auctions (CDAs). Against this background, this paper develops new algorithms that buyer and seller agents can use to participate in CDAs. These algorithms employ heuristic fuzzy rules and fuzzy reasoning mechanisms in order to determine the best bid to make given the state of the marketplace. Moreover, we show how an agent can dynamically adjust its bidding behavior to respond effectively to changes in the supply and demand in the marketplace. We then show, by empirical evaluations, how our agents outperform four of the most prominent algorithms previously developed for CDAs (several of which have been shown to outperform human bidders in experimental studies).