Software services are emerging as the dominant component technology for distributed applications. Using standardized interfaces, clients can remotely access functionality or resources offered by service providers. In e-commerce applications, often such services will be fee-based. Usage metering and Accounting thus form important components of an e-services infrastructure. The metering and accounting problem takes on added complexity with composite e-services - higher-level services built using simpler underlying services, each of which may be independently owned. In this paper we present an architecture for the metering and accounting of composite service usage.