Distributed computing middleware needs to support a wide range of resources, such as diverse software components, various hardware devices, and heterogeneous operating systems and architectures. Current technologies are unable to implement a maintenance-free platform to be compatible with such different computing environments. This situation is presenting an increasing challenge as Grid computing becomes more widespread. The infrastructure of network services (CENSA and CENSI) has been proposed to address this challenge. A seamless Grid computing environment, supported by network services, is composed of various streams such as data, video, audio, and text. We define a mathematical model of capability matching for three-party agreements: requests from users, resources, and network services. Based on the mathematical model, we provide a general approach for capability matching. We also present a new language schema for capability description. As an example, we embed the general matchmaker in the architecture of the access Grid. Several tests of accuracy and performance are discussed.