The Internet is rapidly becoming the preferred mean through which companies provide services to businesses and customers. A large number of eservices, including for instance stock trading, customized newspapers, real-time traffic report, or itinerary planning, is already available on the Web, and the type and number of e-services grows on a daily basis. In order to support the development and deployment of e-services, software vendors are developing eservices frameworks and platforms, that provide a language for describing an eservice, and then allow service providers to register, advertise and securely deliver e-services to (authorized) users. A composite e-service is an e-service defined by composing other basic or composite e-services. As the e-service paradigm becomes popular and more and more applications are developed or deployed as e-services, the need and opportunity for defining composite service become manifest. This paper presents a specific type of e-service (or, rather, a meta e-service) called Composition E-Service (CES), that allows the definition, execution, management, and monitoring of composite e-services. We first describe the advantages and the functionality of such a service. Next, we present the language used for specifying the composition, also discussing why existing workflow languages are not suitable for this purpose. Finally, we present the architecture and implementation of the CES we developed to deliver the service on top of the e-services platform e-speak. An analogous architecture and implementation strategy can be followed with any other e-services platform.