We describe the architecture and initial implementation of the next-generation of Grid Data Management Middleware in the EU DataGrid (EDG) project. The new architecture stems from our experience together with the user requirements gathered during the two years of running our initial set of Grid Data Management Services. All of our new services are based on the Web Service technology paradigm, very much in line with the emerging Open Grid Services Architecture (OGSA). We have modularized our components and invested a great amount of effort in developing secure, extensible and robust services, starting from the design but also using a streamlined build and testing framework. Our service components are: Replica Location Service, Replica Metadata Service, Replica Optimization Service, Replica Subscription and high-level replica management. The service security infrastructure is fully GSI-enabled, hence compatible with the existing Globus Toolkit 2-based services; moreover, it allows for fine-grained authorization mechanisms that can be adjusted depending on the service semantics.