We study an emerging class of high-performance virtual environments, called Real-Time Online Interactive Applications (ROIA), with such popular examples as Massively Multi-player Online Games (MMOG), interactive simulations, virtual communities, etc. ROIA must handle an enormous number of actions from geographically distributed user processes and present to each user a consistent view of the application state. We address a challenging aspect which influences the application scalability-the simultaneous access of several clients and servers to globally replicated objects. The traditional primary-copy-based state replication mechanism ensures fast read access but shows drawbacks for global objects that are concurrently updated by multiple processes. Our main contribution is to combine the traditional statebased approach with a novel operation-based update ordering approach that considers the operation's semantics and allows to use weaker consistency models than the sequential consistency enforced by the primary copy protocol. We implement our improvement of the update concurrency as the Global Object Management System (GOMS) and integrate it into the Real-Time Framework (RTF)-our platform for the high-level development and efficient execution of ROIA which has been used for implementing numerous applications like real-time online MMOG, crowd simulation, etc. Our experiments with GOMS show significant improvements regarding both the usability and the performance of the concurrent updates to replicated global objects.